src/HOL/HOL.thy
author wenzelm
Tue, 03 Mar 2009 14:07:43 +0100
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(*  Title:      HOL/HOL.thy
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    Author:     Tobias Nipkow, Markus Wenzel, and Larry Paulson
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*)
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header {* The basis of Higher-Order Logic *}
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theory HOL
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imports Pure
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uses
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  ("Tools/hologic.ML")
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  "~~/src/Tools/IsaPlanner/zipper.ML"
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  "~~/src/Tools/IsaPlanner/isand.ML"
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  "~~/src/Tools/IsaPlanner/rw_tools.ML"
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  "~~/src/Tools/IsaPlanner/rw_inst.ML"
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  "~~/src/Tools/intuitionistic.ML"
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  "~~/src/Tools/project_rule.ML"
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  "~~/src/Provers/hypsubst.ML"
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  "~~/src/Provers/splitter.ML"
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  "~~/src/Provers/classical.ML"
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  "~~/src/Provers/blast.ML"
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  "~~/src/Provers/clasimp.ML"
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  "~~/src/Tools/coherent.ML"
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  "~~/src/Tools/eqsubst.ML"
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  "~~/src/Provers/quantifier1.ML"
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  ("Tools/simpdata.ML")
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  "~~/src/Tools/random_word.ML"
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  "~~/src/Tools/atomize_elim.ML"
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  "~~/src/Tools/induct.ML"
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  ("~~/src/Tools/induct_tacs.ML")
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  "~~/src/Tools/value.ML"
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  "~~/src/Tools/code/code_name.ML"
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  "~~/src/Tools/code/code_funcgr.ML" (*formal dependency*)
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  "~~/src/Tools/code/code_wellsorted.ML" 
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  "~~/src/Tools/code/code_thingol.ML"
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  "~~/src/Tools/code/code_printer.ML"
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  "~~/src/Tools/code/code_target.ML"
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  "~~/src/Tools/code/code_ml.ML"
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  "~~/src/Tools/code/code_haskell.ML"
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  "~~/src/Tools/nbe.ML"
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  ("Tools/recfun_codegen.ML")
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begin
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setup {* Intuitionistic.method_setup "iprover" *}
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subsection {* Primitive logic *}
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subsubsection {* Core syntax *}
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classes type
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defaultsort type
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setup {* ObjectLogic.add_base_sort @{sort type} *}
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arities
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  "fun" :: (type, type) type
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  itself :: (type) type
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global
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typedecl bool
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judgment
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  Trueprop      :: "bool => prop"                   ("(_)" 5)
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consts
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  Not           :: "bool => bool"                   ("~ _" [40] 40)
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  True          :: bool
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  False         :: bool
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  The           :: "('a => bool) => 'a"
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  All           :: "('a => bool) => bool"           (binder "ALL " 10)
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  Ex            :: "('a => bool) => bool"           (binder "EX " 10)
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  Ex1           :: "('a => bool) => bool"           (binder "EX! " 10)
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  Let           :: "['a, 'a => 'b] => 'b"
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  "op ="        :: "['a, 'a] => bool"               (infixl "=" 50)
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  "op &"        :: "[bool, bool] => bool"           (infixr "&" 35)
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  "op |"        :: "[bool, bool] => bool"           (infixr "|" 30)
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  "op -->"      :: "[bool, bool] => bool"           (infixr "-->" 25)
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local
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consts
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  If            :: "[bool, 'a, 'a] => 'a"           ("(if (_)/ then (_)/ else (_))" 10)
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subsubsection {* Additional concrete syntax *}
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notation (output)
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  "op ="  (infix "=" 50)
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abbreviation
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  not_equal :: "['a, 'a] => bool"  (infixl "~=" 50) where
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  "x ~= y == ~ (x = y)"
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notation (output)
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  not_equal  (infix "~=" 50)
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notation (xsymbols)
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  Not  ("\<not> _" [40] 40) and
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  "op &"  (infixr "\<and>" 35) and
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  "op |"  (infixr "\<or>" 30) and
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  "op -->"  (infixr "\<longrightarrow>" 25) and
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  not_equal  (infix "\<noteq>" 50)
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notation (HTML output)
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  Not  ("\<not> _" [40] 40) and
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  "op &"  (infixr "\<and>" 35) and
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  "op |"  (infixr "\<or>" 30) and
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  not_equal  (infix "\<noteq>" 50)
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abbreviation (iff)
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  iff :: "[bool, bool] => bool"  (infixr "<->" 25) where
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  "A <-> B == A = B"
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notation (xsymbols)
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  iff  (infixr "\<longleftrightarrow>" 25)
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nonterminals
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  letbinds  letbind
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  case_syn  cases_syn
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syntax
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  "_The"        :: "[pttrn, bool] => 'a"                 ("(3THE _./ _)" [0, 10] 10)
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  "_bind"       :: "[pttrn, 'a] => letbind"              ("(2_ =/ _)" 10)
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  ""            :: "letbind => letbinds"                 ("_")
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  "_binds"      :: "[letbind, letbinds] => letbinds"     ("_;/ _")
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  "_Let"        :: "[letbinds, 'a] => 'a"                ("(let (_)/ in (_))" 10)
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  "_case_syntax":: "['a, cases_syn] => 'b"               ("(case _ of/ _)" 10)
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  "_case1"      :: "['a, 'b] => case_syn"                ("(2_ =>/ _)" 10)
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  ""            :: "case_syn => cases_syn"               ("_")
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  "_case2"      :: "[case_syn, cases_syn] => cases_syn"  ("_/ | _")
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translations
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  "THE x. P"              == "The (%x. P)"
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  "_Let (_binds b bs) e"  == "_Let b (_Let bs e)"
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  "let x = a in e"        == "Let a (%x. e)"
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print_translation {*
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(* To avoid eta-contraction of body: *)
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[("The", fn [Abs abs] =>
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     let val (x,t) = atomic_abs_tr' abs
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     in Syntax.const "_The" $ x $ t end)]
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*}
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syntax (xsymbols)
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  "_case1"      :: "['a, 'b] => case_syn"                ("(2_ \<Rightarrow>/ _)" 10)
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notation (xsymbols)
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  All  (binder "\<forall>" 10) and
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  Ex  (binder "\<exists>" 10) and
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  Ex1  (binder "\<exists>!" 10)
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notation (HTML output)
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  All  (binder "\<forall>" 10) and
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  Ex  (binder "\<exists>" 10) and
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  Ex1  (binder "\<exists>!" 10)
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notation (HOL)
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  All  (binder "! " 10) and
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  Ex  (binder "? " 10) and
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  Ex1  (binder "?! " 10)
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36e58620ffc8 replaced HOL_quantifiers flag by "HOL" print mode;
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subsubsection {* Axioms and basic definitions *}
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axioms
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  refl:           "t = (t::'a)"
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  subst:          "s = t \<Longrightarrow> P s \<Longrightarrow> P t"
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  ext:            "(!!x::'a. (f x ::'b) = g x) ==> (%x. f x) = (%x. g x)"
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    -- {*Extensionality is built into the meta-logic, and this rule expresses
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         a related property.  It is an eta-expanded version of the traditional
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         rule, and similar to the ABS rule of HOL*}
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  the_eq_trivial: "(THE x. x = a) = (a::'a)"
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  impI:           "(P ==> Q) ==> P-->Q"
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  mp:             "[| P-->Q;  P |] ==> Q"
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defs
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  True_def:     "True      == ((%x::bool. x) = (%x. x))"
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  All_def:      "All(P)    == (P = (%x. True))"
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  Ex_def:       "Ex(P)     == !Q. (!x. P x --> Q) --> Q"
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  False_def:    "False     == (!P. P)"
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  not_def:      "~ P       == P-->False"
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  and_def:      "P & Q     == !R. (P-->Q-->R) --> R"
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  or_def:       "P | Q     == !R. (P-->R) --> (Q-->R) --> R"
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  Ex1_def:      "Ex1(P)    == ? x. P(x) & (! y. P(y) --> y=x)"
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axioms
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  iff:          "(P-->Q) --> (Q-->P) --> (P=Q)"
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  True_or_False:  "(P=True) | (P=False)"
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defs
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  Let_def:      "Let s f == f(s)"
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  if_def:       "If P x y == THE z::'a. (P=True --> z=x) & (P=False --> z=y)"
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finalconsts
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  "op ="
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  "op -->"
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  The
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axiomatization
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  undefined :: 'a
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abbreviation (input)
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  "arbitrary \<equiv> undefined"
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subsubsection {* Generic classes and algebraic operations *}
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class default =
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  fixes default :: 'a
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class zero = 
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  fixes zero :: 'a  ("0")
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class one =
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  fixes one  :: 'a  ("1")
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hide (open) const zero one
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class plus =
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  fixes plus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "+" 65)
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class minus =
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  fixes minus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "-" 65)
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class uminus =
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  fixes uminus :: "'a \<Rightarrow> 'a"  ("- _" [81] 80)
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class times =
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  fixes times :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "*" 70)
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class inverse =
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  fixes inverse :: "'a \<Rightarrow> 'a"
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    and divide :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "'/" 70)
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class abs =
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  fixes abs :: "'a \<Rightarrow> 'a"
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begin
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notation (xsymbols)
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  abs  ("\<bar>_\<bar>")
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notation (HTML output)
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  abs  ("\<bar>_\<bar>")
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end
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class sgn =
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  fixes sgn :: "'a \<Rightarrow> 'a"
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class ord =
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  fixes less_eq :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
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    and less :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
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begin
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notation
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  less_eq  ("op <=") and
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  less_eq  ("(_/ <= _)" [51, 51] 50) and
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  less  ("op <") and
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  less  ("(_/ < _)"  [51, 51] 50)
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notation (xsymbols)
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  less_eq  ("op \<le>") and
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  less_eq  ("(_/ \<le> _)"  [51, 51] 50)
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notation (HTML output)
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  less_eq  ("op \<le>") and
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  less_eq  ("(_/ \<le> _)"  [51, 51] 50)
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abbreviation (input)
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  greater_eq  (infix ">=" 50) where
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  "x >= y \<equiv> y <= x"
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notation (input)
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  greater_eq  (infix "\<ge>" 50)
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abbreviation (input)
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  greater  (infix ">" 50) where
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  "x > y \<equiv> y < x"
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end
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syntax
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  "_index1"  :: index    ("\<^sub>1")
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translations
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  (index) "\<^sub>1" => (index) "\<^bsub>\<struct>\<^esub>"
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typed_print_translation {*
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let
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  fun tr' c = (c, fn show_sorts => fn T => fn ts =>
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    if (not o null) ts orelse T = dummyT orelse not (! show_types) andalso can Term.dest_Type T then raise Match
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    else Syntax.const Syntax.constrainC $ Syntax.const c $ Syntax.term_of_typ show_sorts T);
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in map tr' [@{const_syntax HOL.one}, @{const_syntax HOL.zero}] end;
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*} -- {* show types that are presumably too general *}
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subsection {* Fundamental rules *}
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subsubsection {* Equality *}
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lemma sym: "s = t ==> t = s"
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  by (erule subst) (rule refl)
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lemma ssubst: "t = s ==> P s ==> P t"
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  by (drule sym) (erule subst)
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lemma trans: "[| r=s; s=t |] ==> r=t"
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   315
  by (erule subst)
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   316
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   317
lemma meta_eq_to_obj_eq: 
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  assumes meq: "A == B"
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  shows "A = B"
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   320
  by (unfold meq) (rule refl)
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   321
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text {* Useful with @{text erule} for proving equalities from known equalities. *}
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   323
     (* a = b
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        |   |
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   325
        c = d   *)
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   326
lemma box_equals: "[| a=b;  a=c;  b=d |] ==> c=d"
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   327
apply (rule trans)
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   328
apply (rule trans)
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apply (rule sym)
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   330
apply assumption+
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   331
done
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   332
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2ef571f80a55 Moved oderings from HOL into the new Orderings.thy
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   333
text {* For calculational reasoning: *}
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   334
2ef571f80a55 Moved oderings from HOL into the new Orderings.thy
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   335
lemma forw_subst: "a = b ==> P b ==> P a"
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   336
  by (rule ssubst)
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   337
2ef571f80a55 Moved oderings from HOL into the new Orderings.thy
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   338
lemma back_subst: "P a ==> a = b ==> P b"
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   339
  by (rule subst)
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   340
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   341
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   342
subsubsection {*Congruence rules for application*}
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   343
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   344
(*similar to AP_THM in Gordon's HOL*)
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   345
lemma fun_cong: "(f::'a=>'b) = g ==> f(x)=g(x)"
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   346
apply (erule subst)
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   347
apply (rule refl)
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   348
done
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   349
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   350
(*similar to AP_TERM in Gordon's HOL and FOL's subst_context*)
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   351
lemma arg_cong: "x=y ==> f(x)=f(y)"
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   352
apply (erule subst)
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   353
apply (rule refl)
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   354
done
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diff changeset
   355
15655
157f3988f775 arg_cong2 by Norbert Voelker
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   356
lemma arg_cong2: "\<lbrakk> a = b; c = d \<rbrakk> \<Longrightarrow> f a c = f b d"
157f3988f775 arg_cong2 by Norbert Voelker
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   357
apply (erule ssubst)+
157f3988f775 arg_cong2 by Norbert Voelker
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   358
apply (rule refl)
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   359
done
157f3988f775 arg_cong2 by Norbert Voelker
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parents: 15570
diff changeset
   360
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   361
lemma cong: "[| f = g; (x::'a) = y |] ==> f(x) = g(y)"
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   362
apply (erule subst)+
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diff changeset
   363
apply (rule refl)
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   364
done
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parents: 15380
diff changeset
   365
1d195de59497 removal of HOL_Lemmas
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   366
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   367
subsubsection {*Equality of booleans -- iff*}
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   368
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   369
lemma iffI: assumes "P ==> Q" and "Q ==> P" shows "P=Q"
9c97af4a1567 tuned proofs;
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   370
  by (iprover intro: iff [THEN mp, THEN mp] impI assms)
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   371
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   372
lemma iffD2: "[| P=Q; Q |] ==> P"
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356a9f711899 structure ProjectRule;
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   373
  by (erule ssubst)
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   374
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   375
lemma rev_iffD2: "[| Q; P=Q |] ==> P"
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356a9f711899 structure ProjectRule;
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   376
  by (erule iffD2)
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   377
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9c97af4a1567 tuned proofs;
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   378
lemma iffD1: "Q = P \<Longrightarrow> Q \<Longrightarrow> P"
9c97af4a1567 tuned proofs;
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   379
  by (drule sym) (rule iffD2)
9c97af4a1567 tuned proofs;
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parents: 21502
diff changeset
   380
9c97af4a1567 tuned proofs;
wenzelm
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   381
lemma rev_iffD1: "Q \<Longrightarrow> Q = P \<Longrightarrow> P"
9c97af4a1567 tuned proofs;
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parents: 21502
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   382
  by (drule sym) (rule rev_iffD2)
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diff changeset
   383
1d195de59497 removal of HOL_Lemmas
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diff changeset
   384
lemma iffE:
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   385
  assumes major: "P=Q"
21504
9c97af4a1567 tuned proofs;
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parents: 21502
diff changeset
   386
    and minor: "[| P --> Q; Q --> P |] ==> R"
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
   387
  shows R
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
   388
  by (iprover intro: minor impI major [THEN iffD2] major [THEN iffD1])
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parents: 15380
diff changeset
   389
1d195de59497 removal of HOL_Lemmas
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diff changeset
   390
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   391
subsubsection {*True*}
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diff changeset
   392
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diff changeset
   393
lemma TrueI: "True"
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   394
  unfolding True_def by (rule refl)
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diff changeset
   395
21504
9c97af4a1567 tuned proofs;
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parents: 21502
diff changeset
   396
lemma eqTrueI: "P ==> P = True"
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
   397
  by (iprover intro: iffI TrueI)
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paulson
parents: 15380
diff changeset
   398
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   399
lemma eqTrueE: "P = True ==> P"
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   400
  by (erule iffD2) (rule TrueI)
15411
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paulson
parents: 15380
diff changeset
   401
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   402
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34b2c1bb7178 cleanup basic HOL bootstrap
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diff changeset
   403
subsubsection {*Universal quantifier*}
15411
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paulson
parents: 15380
diff changeset
   404
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   405
lemma allI: assumes "!!x::'a. P(x)" shows "ALL x. P(x)"
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   406
  unfolding All_def by (iprover intro: ext eqTrueI assms)
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diff changeset
   407
1d195de59497 removal of HOL_Lemmas
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diff changeset
   408
lemma spec: "ALL x::'a. P(x) ==> P(x)"
1d195de59497 removal of HOL_Lemmas
paulson
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diff changeset
   409
apply (unfold All_def)
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parents: 15380
diff changeset
   410
apply (rule eqTrueE)
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diff changeset
   411
apply (erule fun_cong)
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diff changeset
   412
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   413
1d195de59497 removal of HOL_Lemmas
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diff changeset
   414
lemma allE:
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   415
  assumes major: "ALL x. P(x)"
21504
9c97af4a1567 tuned proofs;
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parents: 21502
diff changeset
   416
    and minor: "P(x) ==> R"
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   417
  shows R
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   418
  by (iprover intro: minor major [THEN spec])
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diff changeset
   419
1d195de59497 removal of HOL_Lemmas
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diff changeset
   420
lemma all_dupE:
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   421
  assumes major: "ALL x. P(x)"
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   422
    and minor: "[| P(x); ALL x. P(x) |] ==> R"
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   423
  shows R
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   424
  by (iprover intro: minor major major [THEN spec])
15411
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parents: 15380
diff changeset
   425
1d195de59497 removal of HOL_Lemmas
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diff changeset
   426
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   427
subsubsection {* False *}
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   428
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   429
text {*
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   430
  Depends upon @{text spec}; it is impossible to do propositional
9c97af4a1567 tuned proofs;
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parents: 21502
diff changeset
   431
  logic before quantifiers!
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   432
*}
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diff changeset
   433
1d195de59497 removal of HOL_Lemmas
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diff changeset
   434
lemma FalseE: "False ==> P"
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   435
  apply (unfold False_def)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   436
  apply (erule spec)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   437
  done
15411
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paulson
parents: 15380
diff changeset
   438
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   439
lemma False_neq_True: "False = True ==> P"
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   440
  by (erule eqTrueE [THEN FalseE])
15411
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paulson
parents: 15380
diff changeset
   441
1d195de59497 removal of HOL_Lemmas
paulson
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diff changeset
   442
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   443
subsubsection {* Negation *}
15411
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parents: 15380
diff changeset
   444
1d195de59497 removal of HOL_Lemmas
paulson
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diff changeset
   445
lemma notI:
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   446
  assumes "P ==> False"
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   447
  shows "~P"
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   448
  apply (unfold not_def)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   449
  apply (iprover intro: impI assms)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   450
  done
15411
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paulson
parents: 15380
diff changeset
   451
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   452
lemma False_not_True: "False ~= True"
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   453
  apply (rule notI)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   454
  apply (erule False_neq_True)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   455
  done
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   456
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   457
lemma True_not_False: "True ~= False"
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   458
  apply (rule notI)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   459
  apply (drule sym)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   460
  apply (erule False_neq_True)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   461
  done
15411
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paulson
parents: 15380
diff changeset
   462
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   463
lemma notE: "[| ~P;  P |] ==> R"
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   464
  apply (unfold not_def)
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   465
  apply (erule mp [THEN FalseE])
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   466
  apply assumption
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   467
  done
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   468
21504
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   469
lemma notI2: "(P \<Longrightarrow> \<not> Pa) \<Longrightarrow> (P \<Longrightarrow> Pa) \<Longrightarrow> \<not> P"
9c97af4a1567 tuned proofs;
wenzelm
parents: 21502
diff changeset
   470
  by (erule notE [THEN notI]) (erule meta_mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   471
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   472
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   473
subsubsection {*Implication*}
15411
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paulson
parents: 15380
diff changeset
   474
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   475
lemma impE:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   476
  assumes "P-->Q" "P" "Q ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   477
  shows "R"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   478
by (iprover intro: assms mp)
15411
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paulson
parents: 15380
diff changeset
   479
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   480
(* Reduces Q to P-->Q, allowing substitution in P. *)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   481
lemma rev_mp: "[| P;  P --> Q |] ==> Q"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   482
by (iprover intro: mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   483
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   484
lemma contrapos_nn:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   485
  assumes major: "~Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   486
      and minor: "P==>Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   487
  shows "~P"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   488
by (iprover intro: notI minor major [THEN notE])
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   489
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   490
(*not used at all, but we already have the other 3 combinations *)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   491
lemma contrapos_pn:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   492
  assumes major: "Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   493
      and minor: "P ==> ~Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   494
  shows "~P"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   495
by (iprover intro: notI minor major notE)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   496
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   497
lemma not_sym: "t ~= s ==> s ~= t"
21250
a268f6288fb6 moved lemma eq_neq_eq_imp_neq to HOL
haftmann
parents: 21218
diff changeset
   498
  by (erule contrapos_nn) (erule sym)
a268f6288fb6 moved lemma eq_neq_eq_imp_neq to HOL
haftmann
parents: 21218
diff changeset
   499
a268f6288fb6 moved lemma eq_neq_eq_imp_neq to HOL
haftmann
parents: 21218
diff changeset
   500
lemma eq_neq_eq_imp_neq: "[| x = a ; a ~= b; b = y |] ==> x ~= y"
a268f6288fb6 moved lemma eq_neq_eq_imp_neq to HOL
haftmann
parents: 21218
diff changeset
   501
  by (erule subst, erule ssubst, assumption)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   502
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   503
(*still used in HOLCF*)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   504
lemma rev_contrapos:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   505
  assumes pq: "P ==> Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   506
      and nq: "~Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   507
  shows "~P"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   508
apply (rule nq [THEN contrapos_nn])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   509
apply (erule pq)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   510
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   511
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   512
subsubsection {*Existential quantifier*}
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   513
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   514
lemma exI: "P x ==> EX x::'a. P x"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   515
apply (unfold Ex_def)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   516
apply (iprover intro: allI allE impI mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   517
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   518
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   519
lemma exE:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   520
  assumes major: "EX x::'a. P(x)"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   521
      and minor: "!!x. P(x) ==> Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   522
  shows "Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   523
apply (rule major [unfolded Ex_def, THEN spec, THEN mp])
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   524
apply (iprover intro: impI [THEN allI] minor)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   525
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   526
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   527
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   528
subsubsection {*Conjunction*}
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   529
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   530
lemma conjI: "[| P; Q |] ==> P&Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   531
apply (unfold and_def)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   532
apply (iprover intro: impI [THEN allI] mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   533
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   534
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   535
lemma conjunct1: "[| P & Q |] ==> P"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   536
apply (unfold and_def)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   537
apply (iprover intro: impI dest: spec mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   538
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   539
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   540
lemma conjunct2: "[| P & Q |] ==> Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   541
apply (unfold and_def)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   542
apply (iprover intro: impI dest: spec mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   543
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   544
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   545
lemma conjE:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   546
  assumes major: "P&Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   547
      and minor: "[| P; Q |] ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   548
  shows "R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   549
apply (rule minor)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   550
apply (rule major [THEN conjunct1])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   551
apply (rule major [THEN conjunct2])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   552
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   553
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   554
lemma context_conjI:
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   555
  assumes "P" "P ==> Q" shows "P & Q"
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   556
by (iprover intro: conjI assms)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   557
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   558
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   559
subsubsection {*Disjunction*}
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   560
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   561
lemma disjI1: "P ==> P|Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   562
apply (unfold or_def)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   563
apply (iprover intro: allI impI mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   564
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   565
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   566
lemma disjI2: "Q ==> P|Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   567
apply (unfold or_def)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   568
apply (iprover intro: allI impI mp)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   569
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   570
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   571
lemma disjE:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   572
  assumes major: "P|Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   573
      and minorP: "P ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   574
      and minorQ: "Q ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   575
  shows "R"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   576
by (iprover intro: minorP minorQ impI
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   577
                 major [unfolded or_def, THEN spec, THEN mp, THEN mp])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   578
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   579
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   580
subsubsection {*Classical logic*}
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   581
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   582
lemma classical:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   583
  assumes prem: "~P ==> P"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   584
  shows "P"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   585
apply (rule True_or_False [THEN disjE, THEN eqTrueE])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   586
apply assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   587
apply (rule notI [THEN prem, THEN eqTrueI])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   588
apply (erule subst)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   589
apply assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   590
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   591
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   592
lemmas ccontr = FalseE [THEN classical, standard]
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   593
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   594
(*notE with premises exchanged; it discharges ~R so that it can be used to
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   595
  make elimination rules*)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   596
lemma rev_notE:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   597
  assumes premp: "P"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   598
      and premnot: "~R ==> ~P"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   599
  shows "R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   600
apply (rule ccontr)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   601
apply (erule notE [OF premnot premp])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   602
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   603
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   604
(*Double negation law*)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   605
lemma notnotD: "~~P ==> P"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   606
apply (rule classical)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   607
apply (erule notE)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   608
apply assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   609
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   610
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   611
lemma contrapos_pp:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   612
  assumes p1: "Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   613
      and p2: "~P ==> ~Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   614
  shows "P"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   615
by (iprover intro: classical p1 p2 notE)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   616
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   617
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   618
subsubsection {*Unique existence*}
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   619
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   620
lemma ex1I:
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   621
  assumes "P a" "!!x. P(x) ==> x=a"
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   622
  shows "EX! x. P(x)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   623
by (unfold Ex1_def, iprover intro: assms exI conjI allI impI)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   624
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   625
text{*Sometimes easier to use: the premises have no shared variables.  Safe!*}
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   626
lemma ex_ex1I:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   627
  assumes ex_prem: "EX x. P(x)"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   628
      and eq: "!!x y. [| P(x); P(y) |] ==> x=y"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   629
  shows "EX! x. P(x)"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   630
by (iprover intro: ex_prem [THEN exE] ex1I eq)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   631
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   632
lemma ex1E:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   633
  assumes major: "EX! x. P(x)"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   634
      and minor: "!!x. [| P(x);  ALL y. P(y) --> y=x |] ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   635
  shows "R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   636
apply (rule major [unfolded Ex1_def, THEN exE])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   637
apply (erule conjE)
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   638
apply (iprover intro: minor)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   639
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   640
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   641
lemma ex1_implies_ex: "EX! x. P x ==> EX x. P x"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   642
apply (erule ex1E)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   643
apply (rule exI)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   644
apply assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   645
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   646
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   647
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   648
subsubsection {*THE: definite description operator*}
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   649
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   650
lemma the_equality:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   651
  assumes prema: "P a"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   652
      and premx: "!!x. P x ==> x=a"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   653
  shows "(THE x. P x) = a"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   654
apply (rule trans [OF _ the_eq_trivial])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   655
apply (rule_tac f = "The" in arg_cong)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   656
apply (rule ext)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   657
apply (rule iffI)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   658
 apply (erule premx)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   659
apply (erule ssubst, rule prema)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   660
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   661
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   662
lemma theI:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   663
  assumes "P a" and "!!x. P x ==> x=a"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   664
  shows "P (THE x. P x)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   665
by (iprover intro: assms the_equality [THEN ssubst])
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   666
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   667
lemma theI': "EX! x. P x ==> P (THE x. P x)"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   668
apply (erule ex1E)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   669
apply (erule theI)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   670
apply (erule allE)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   671
apply (erule mp)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   672
apply assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   673
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   674
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   675
(*Easier to apply than theI: only one occurrence of P*)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   676
lemma theI2:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   677
  assumes "P a" "!!x. P x ==> x=a" "!!x. P x ==> Q x"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   678
  shows "Q (THE x. P x)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   679
by (iprover intro: assms theI)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   680
24553
9b19da7b2b08 added lemma
nipkow
parents: 24506
diff changeset
   681
lemma the1I2: assumes "EX! x. P x" "\<And>x. P x \<Longrightarrow> Q x" shows "Q (THE x. P x)"
9b19da7b2b08 added lemma
nipkow
parents: 24506
diff changeset
   682
by(iprover intro:assms(2) theI2[where P=P and Q=Q] ex1E[OF assms(1)]
9b19da7b2b08 added lemma
nipkow
parents: 24506
diff changeset
   683
           elim:allE impE)
9b19da7b2b08 added lemma
nipkow
parents: 24506
diff changeset
   684
18697
86b3f73e3fd5 declare the1_equality [elim?];
wenzelm
parents: 18689
diff changeset
   685
lemma the1_equality [elim?]: "[| EX!x. P x; P a |] ==> (THE x. P x) = a"
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   686
apply (rule the_equality)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   687
apply  assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   688
apply (erule ex1E)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   689
apply (erule all_dupE)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   690
apply (drule mp)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   691
apply  assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   692
apply (erule ssubst)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   693
apply (erule allE)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   694
apply (erule mp)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   695
apply assumption
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   696
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   697
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   698
lemma the_sym_eq_trivial: "(THE y. x=y) = x"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   699
apply (rule the_equality)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   700
apply (rule refl)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   701
apply (erule sym)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   702
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   703
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   704
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   705
subsubsection {*Classical intro rules for disjunction and existential quantifiers*}
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   706
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   707
lemma disjCI:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   708
  assumes "~Q ==> P" shows "P|Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   709
apply (rule classical)
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   710
apply (iprover intro: assms disjI1 disjI2 notI elim: notE)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   711
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   712
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   713
lemma excluded_middle: "~P | P"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   714
by (iprover intro: disjCI)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   715
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   716
text {*
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   717
  case distinction as a natural deduction rule.
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   718
  Note that @{term "~P"} is the second case, not the first
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   719
*}
27126
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
   720
lemma case_split [case_names True False]:
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   721
  assumes prem1: "P ==> Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   722
      and prem2: "~P ==> Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   723
  shows "Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   724
apply (rule excluded_middle [THEN disjE])
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   725
apply (erule prem2)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   726
apply (erule prem1)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   727
done
27126
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
   728
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   729
(*Classical implies (-->) elimination. *)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   730
lemma impCE:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   731
  assumes major: "P-->Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   732
      and minor: "~P ==> R" "Q ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   733
  shows "R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   734
apply (rule excluded_middle [of P, THEN disjE])
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   735
apply (iprover intro: minor major [THEN mp])+
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   736
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   737
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   738
(*This version of --> elimination works on Q before P.  It works best for
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   739
  those cases in which P holds "almost everywhere".  Can't install as
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   740
  default: would break old proofs.*)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   741
lemma impCE':
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   742
  assumes major: "P-->Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   743
      and minor: "Q ==> R" "~P ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   744
  shows "R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   745
apply (rule excluded_middle [of P, THEN disjE])
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   746
apply (iprover intro: minor major [THEN mp])+
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   747
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   748
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   749
(*Classical <-> elimination. *)
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   750
lemma iffCE:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   751
  assumes major: "P=Q"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   752
      and minor: "[| P; Q |] ==> R"  "[| ~P; ~Q |] ==> R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   753
  shows "R"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   754
apply (rule major [THEN iffE])
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
   755
apply (iprover intro: minor elim: impCE notE)
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   756
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   757
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   758
lemma exCI:
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   759
  assumes "ALL x. ~P(x) ==> P(a)"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   760
  shows "EX x. P(x)"
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   761
apply (rule ccontr)
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   762
apply (iprover intro: assms exI allI notI notE [of "\<exists>x. P x"])
15411
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   763
done
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   764
1d195de59497 removal of HOL_Lemmas
paulson
parents: 15380
diff changeset
   765
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   766
subsubsection {* Intuitionistic Reasoning *}
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   767
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   768
lemma impE':
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   769
  assumes 1: "P --> Q"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   770
    and 2: "Q ==> R"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   771
    and 3: "P --> Q ==> P"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   772
  shows R
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   773
proof -
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   774
  from 3 and 1 have P .
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   775
  with 1 have Q by (rule impE)
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   776
  with 2 show R .
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   777
qed
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   778
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   779
lemma allE':
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   780
  assumes 1: "ALL x. P x"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   781
    and 2: "P x ==> ALL x. P x ==> Q"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   782
  shows Q
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   783
proof -
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   784
  from 1 have "P x" by (rule spec)
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   785
  from this and 1 show Q by (rule 2)
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   786
qed
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   787
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   788
lemma notE':
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   789
  assumes 1: "~ P"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   790
    and 2: "~ P ==> P"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
   791
  shows R
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   792
proof -
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   793
  from 2 and 1 have P .
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   794
  with 1 show R by (rule notE)
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   795
qed
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   796
22444
fb80fedd192d added safe intro rules for removing "True" subgoals as well as "~ False" ones.
dixon
parents: 22377
diff changeset
   797
lemma TrueE: "True ==> P ==> P" .
fb80fedd192d added safe intro rules for removing "True" subgoals as well as "~ False" ones.
dixon
parents: 22377
diff changeset
   798
lemma notFalseE: "~ False ==> P ==> P" .
fb80fedd192d added safe intro rules for removing "True" subgoals as well as "~ False" ones.
dixon
parents: 22377
diff changeset
   799
22467
c9357ef01168 TrueElim and notTrueElim tested and added as safe elim rules.
dixon
parents: 22445
diff changeset
   800
lemmas [Pure.elim!] = disjE iffE FalseE conjE exE TrueE notFalseE
15801
d2f5ca3c048d superceded by Pure.thy and CPure.thy;
wenzelm
parents: 15676
diff changeset
   801
  and [Pure.intro!] = iffI conjI impI TrueI notI allI refl
d2f5ca3c048d superceded by Pure.thy and CPure.thy;
wenzelm
parents: 15676
diff changeset
   802
  and [Pure.elim 2] = allE notE' impE'
d2f5ca3c048d superceded by Pure.thy and CPure.thy;
wenzelm
parents: 15676
diff changeset
   803
  and [Pure.intro] = exI disjI2 disjI1
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   804
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   805
lemmas [trans] = trans
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   806
  and [sym] = sym not_sym
15801
d2f5ca3c048d superceded by Pure.thy and CPure.thy;
wenzelm
parents: 15676
diff changeset
   807
  and [Pure.elim?] = iffD1 iffD2 impE
11750
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   808
28952
15a4b2cf8c34 made repository layout more coherent with logical distribution structure; stripped some $Id$s
haftmann
parents: 28856
diff changeset
   809
use "Tools/hologic.ML"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   810
11438
3d9222b80989 declare trans [trans] (*overridden in theory Calculation*);
wenzelm
parents: 11432
diff changeset
   811
11750
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   812
subsubsection {* Atomizing meta-level connectives *}
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   813
28513
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
   814
axiomatization where
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
   815
  eq_reflection: "x = y \<Longrightarrow> x \<equiv> y" (*admissible axiom*)
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
   816
11750
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   817
lemma atomize_all [atomize]: "(!!x. P x) == Trueprop (ALL x. P x)"
12003
c09427e5f554 removed obsolete (rule equal_intr_rule);
wenzelm
parents: 11989
diff changeset
   818
proof
9488
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   819
  assume "!!x. P x"
23389
aaca6a8e5414 tuned proofs: avoid implicit prems;
wenzelm
parents: 23263
diff changeset
   820
  then show "ALL x. P x" ..
9488
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   821
next
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   822
  assume "ALL x. P x"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   823
  then show "!!x. P x" by (rule allE)
9488
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   824
qed
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   825
11750
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   826
lemma atomize_imp [atomize]: "(A ==> B) == Trueprop (A --> B)"
12003
c09427e5f554 removed obsolete (rule equal_intr_rule);
wenzelm
parents: 11989
diff changeset
   827
proof
9488
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   828
  assume r: "A ==> B"
10383
a092ae7bb2a6 "atomize" for classical tactics;
wenzelm
parents: 9970
diff changeset
   829
  show "A --> B" by (rule impI) (rule r)
9488
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   830
next
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   831
  assume "A --> B" and A
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   832
  then show B by (rule mp)
9488
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   833
qed
f11bece4e2db added all_eq, imp_eq (for blast);
wenzelm
parents: 9352
diff changeset
   834
14749
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   835
lemma atomize_not: "(A ==> False) == Trueprop (~A)"
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   836
proof
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   837
  assume r: "A ==> False"
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   838
  show "~A" by (rule notI) (rule r)
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   839
next
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   840
  assume "~A" and A
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   841
  then show False by (rule notE)
14749
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   842
qed
9ccfd0f59e11 new atomize theorem
paulson
parents: 14690
diff changeset
   843
11750
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   844
lemma atomize_eq [atomize]: "(x == y) == Trueprop (x = y)"
12003
c09427e5f554 removed obsolete (rule equal_intr_rule);
wenzelm
parents: 11989
diff changeset
   845
proof
10432
3dfbc913d184 added axclass inverse and consts inverse, divide (infix "/");
wenzelm
parents: 10383
diff changeset
   846
  assume "x == y"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   847
  show "x = y" by (unfold `x == y`) (rule refl)
10432
3dfbc913d184 added axclass inverse and consts inverse, divide (infix "/");
wenzelm
parents: 10383
diff changeset
   848
next
3dfbc913d184 added axclass inverse and consts inverse, divide (infix "/");
wenzelm
parents: 10383
diff changeset
   849
  assume "x = y"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
   850
  then show "x == y" by (rule eq_reflection)
10432
3dfbc913d184 added axclass inverse and consts inverse, divide (infix "/");
wenzelm
parents: 10383
diff changeset
   851
qed
3dfbc913d184 added axclass inverse and consts inverse, divide (infix "/");
wenzelm
parents: 10383
diff changeset
   852
28856
5e009a80fe6d Pure syntax: more coherent treatment of aprop, permanent TERM and &&&;
wenzelm
parents: 28741
diff changeset
   853
lemma atomize_conj [atomize]: "(A &&& B) == Trueprop (A & B)"
12003
c09427e5f554 removed obsolete (rule equal_intr_rule);
wenzelm
parents: 11989
diff changeset
   854
proof
28856
5e009a80fe6d Pure syntax: more coherent treatment of aprop, permanent TERM and &&&;
wenzelm
parents: 28741
diff changeset
   855
  assume conj: "A &&& B"
19121
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   856
  show "A & B"
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   857
  proof (rule conjI)
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   858
    from conj show A by (rule conjunctionD1)
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   859
    from conj show B by (rule conjunctionD2)
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   860
  qed
11953
f98623fdf6ef atomize_conj;
wenzelm
parents: 11824
diff changeset
   861
next
19121
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   862
  assume conj: "A & B"
28856
5e009a80fe6d Pure syntax: more coherent treatment of aprop, permanent TERM and &&&;
wenzelm
parents: 28741
diff changeset
   863
  show "A &&& B"
19121
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   864
  proof -
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   865
    from conj show A ..
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19039
diff changeset
   866
    from conj show B ..
11953
f98623fdf6ef atomize_conj;
wenzelm
parents: 11824
diff changeset
   867
  qed
f98623fdf6ef atomize_conj;
wenzelm
parents: 11824
diff changeset
   868
qed
f98623fdf6ef atomize_conj;
wenzelm
parents: 11824
diff changeset
   869
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   870
lemmas [symmetric, rulify] = atomize_all atomize_imp
18832
6ab4de872a70 declare 'defn' rules;
wenzelm
parents: 18757
diff changeset
   871
  and [symmetric, defn] = atomize_all atomize_imp atomize_eq
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   872
11750
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   873
26580
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   874
subsubsection {* Atomizing elimination rules *}
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   875
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   876
setup AtomizeElim.setup
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   877
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   878
lemma atomize_exL[atomize_elim]: "(!!x. P x ==> Q) == ((EX x. P x) ==> Q)"
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   879
  by rule iprover+
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   880
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   881
lemma atomize_conjL[atomize_elim]: "(A ==> B ==> C) == (A & B ==> C)"
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   882
  by rule iprover+
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   883
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   884
lemma atomize_disjL[atomize_elim]: "((A ==> C) ==> (B ==> C) ==> C) == ((A | B ==> C) ==> C)"
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   885
  by rule iprover+
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   886
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   887
lemma atomize_elimL[atomize_elim]: "(!!B. (A ==> B) ==> B) == Trueprop A" ..
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   888
c3e597a476fd Generic conversion and tactic "atomize_elim" to convert elimination rules
krauss
parents: 26555
diff changeset
   889
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   890
subsection {* Package setup *}
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   891
11750
3e400964893e judgment Trueprop;
wenzelm
parents: 11724
diff changeset
   892
subsubsection {* Classical Reasoner setup *}
9529
d9434a9277a4 lemmas atomize = all_eq imp_eq;
wenzelm
parents: 9488
diff changeset
   893
26411
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   894
lemma imp_elim: "P --> Q ==> (~ R ==> P) ==> (Q ==> R) ==> R"
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   895
  by (rule classical) iprover
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   896
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   897
lemma swap: "~ P ==> (~ R ==> P) ==> R"
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   898
  by (rule classical) iprover
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   899
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   900
lemma thin_refl:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   901
  "\<And>X. \<lbrakk> x=x; PROP W \<rbrakk> \<Longrightarrow> PROP W" .
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   902
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   903
ML {*
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   904
structure Hypsubst = HypsubstFun(
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   905
struct
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   906
  structure Simplifier = Simplifier
21218
38013c3a77a2 tuned hypsubst setup;
wenzelm
parents: 21210
diff changeset
   907
  val dest_eq = HOLogic.dest_eq
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   908
  val dest_Trueprop = HOLogic.dest_Trueprop
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   909
  val dest_imp = HOLogic.dest_imp
26411
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   910
  val eq_reflection = @{thm eq_reflection}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   911
  val rev_eq_reflection = @{thm meta_eq_to_obj_eq}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   912
  val imp_intr = @{thm impI}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   913
  val rev_mp = @{thm rev_mp}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   914
  val subst = @{thm subst}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   915
  val sym = @{thm sym}
22129
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
   916
  val thin_refl = @{thm thin_refl};
27572
67cd6ed76446 single_hyp(_meta)_subst_tac: Controlled substitution of a single hyp
krauss
parents: 27338
diff changeset
   917
  val prop_subst = @{lemma "PROP P t ==> PROP prop (x = t ==> PROP P x)"
67cd6ed76446 single_hyp(_meta)_subst_tac: Controlled substitution of a single hyp
krauss
parents: 27338
diff changeset
   918
                     by (unfold prop_def) (drule eq_reflection, unfold)}
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   919
end);
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
   920
open Hypsubst;
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   921
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   922
structure Classical = ClassicalFun(
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   923
struct
26411
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   924
  val imp_elim = @{thm imp_elim}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   925
  val not_elim = @{thm notE}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   926
  val swap = @{thm swap}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
   927
  val classical = @{thm classical}
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   928
  val sizef = Drule.size_of_thm
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   929
  val hyp_subst_tacs = [Hypsubst.hyp_subst_tac]
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   930
end);
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   931
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   932
structure BasicClassical: BASIC_CLASSICAL = Classical; 
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
   933
open BasicClassical;
22129
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
   934
27338
2cd6c60cc10b ML_Antiquote.value;
wenzelm
parents: 27326
diff changeset
   935
ML_Antiquote.value "claset"
2cd6c60cc10b ML_Antiquote.value;
wenzelm
parents: 27326
diff changeset
   936
  (Scan.succeed "Classical.local_claset_of (ML_Context.the_local_context ())");
24035
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
   937
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
   938
structure ResAtpset = NamedThmsFun(val name = "atp" val description = "ATP rules");
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24280
diff changeset
   939
29869
a7a8b90cd882 Renamed descriptions of Nitpick (and ATP) attributes, so that they fit well with the rest of the sentence in ProofGeneral.
blanchet
parents: 29868
diff changeset
   940
structure ResBlacklist = NamedThmsFun(val name = "noatp" val description = "theorems blacklisted for ATP");
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   941
*}
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   942
25388
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
   943
text {*ResBlacklist holds theorems blacklisted to sledgehammer. 
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24280
diff changeset
   944
  These theorems typically produce clauses that are prolific (match too many equality or
25388
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
   945
  membership literals) and relate to seldom-used facts. Some duplicate other rules.*}
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24280
diff changeset
   946
21009
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   947
setup {*
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   948
let
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   949
  (*prevent substitution on bool*)
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   950
  fun hyp_subst_tac' i thm = if i <= Thm.nprems_of thm andalso
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   951
    Term.exists_Const (fn ("op =", Type (_, [T, _])) => T <> Type ("bool", []) | _ => false)
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   952
      (nth (Thm.prems_of thm) (i - 1)) then Hypsubst.hyp_subst_tac i thm else no_tac thm;
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   953
in
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   954
  Hypsubst.hypsubst_setup
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   955
  #> ContextRules.addSWrapper (fn tac => hyp_subst_tac' ORELSE' tac)
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   956
  #> Classical.setup
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
   957
  #> ResAtpset.setup
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24280
diff changeset
   958
  #> ResBlacklist.setup
21009
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   959
end
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   960
*}
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   961
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   962
declare iffI [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   963
  and notI [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   964
  and impI [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   965
  and disjCI [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   966
  and conjI [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   967
  and TrueI [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   968
  and refl [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   969
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   970
declare iffCE [elim!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   971
  and FalseE [elim!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   972
  and impCE [elim!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   973
  and disjE [elim!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   974
  and conjE [elim!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   975
  and conjE [elim!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   976
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   977
declare ex_ex1I [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   978
  and allI [intro!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   979
  and the_equality [intro]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   980
  and exI [intro]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   981
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   982
declare exE [elim!]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   983
  allE [elim]
0eae3fb48936 lifted claset setup from ML to Isar level
haftmann
parents: 20973
diff changeset
   984
22377
61610b1beedf tuned ML setup;
wenzelm
parents: 22218
diff changeset
   985
ML {* val HOL_cs = @{claset} *}
19162
67436e2a16df Added setup for "atpset" (a rule set for ATPs).
mengj
parents: 19138
diff changeset
   986
20223
89d2758ecddf tuned proofs;
wenzelm
parents: 20172
diff changeset
   987
lemma contrapos_np: "~ Q ==> (~ P ==> Q) ==> P"
89d2758ecddf tuned proofs;
wenzelm
parents: 20172
diff changeset
   988
  apply (erule swap)
89d2758ecddf tuned proofs;
wenzelm
parents: 20172
diff changeset
   989
  apply (erule (1) meta_mp)
89d2758ecddf tuned proofs;
wenzelm
parents: 20172
diff changeset
   990
  done
10383
a092ae7bb2a6 "atomize" for classical tactics;
wenzelm
parents: 9970
diff changeset
   991
18689
a50587cd8414 prefer ex1I over ex_ex1I in single-step reasoning;
wenzelm
parents: 18595
diff changeset
   992
declare ex_ex1I [rule del, intro! 2]
a50587cd8414 prefer ex1I over ex_ex1I in single-step reasoning;
wenzelm
parents: 18595
diff changeset
   993
  and ex1I [intro]
a50587cd8414 prefer ex1I over ex_ex1I in single-step reasoning;
wenzelm
parents: 18595
diff changeset
   994
12386
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   995
lemmas [intro?] = ext
9c38ec9eca1c tuned declarations (rules, sym, etc.);
wenzelm
parents: 12354
diff changeset
   996
  and [elim?] = ex1_implies_ex
11977
2e7c54b86763 tuned declaration of rules;
wenzelm
parents: 11953
diff changeset
   997
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
   998
(*Better then ex1E for classical reasoner: needs no quantifier duplication!*)
20973
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
   999
lemma alt_ex1E [elim!]:
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1000
  assumes major: "\<exists>!x. P x"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1001
      and prem: "\<And>x. \<lbrakk> P x; \<forall>y y'. P y \<and> P y' \<longrightarrow> y = y' \<rbrakk> \<Longrightarrow> R"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1002
  shows R
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1003
apply (rule ex1E [OF major])
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1004
apply (rule prem)
22129
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1005
apply (tactic {* ares_tac @{thms allI} 1 *})+
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1006
apply (tactic {* etac (Classical.dup_elim @{thm allE}) 1 *})
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1007
apply iprover
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1008
done
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1009
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1010
ML {*
25388
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
  1011
structure Blast = BlastFun
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
  1012
(
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1013
  type claset = Classical.claset
22744
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22481
diff changeset
  1014
  val equality_name = @{const_name "op ="}
22993
haftmann
parents: 22839
diff changeset
  1015
  val not_name = @{const_name Not}
26411
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
  1016
  val notE = @{thm notE}
cd74690f3bfb pass imp_elim, swap to classical prover;
wenzelm
parents: 25966
diff changeset
  1017
  val ccontr = @{thm ccontr}
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1018
  val contr_tac = Classical.contr_tac
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1019
  val dup_intr = Classical.dup_intr
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1020
  val hyp_subst_tac = Hypsubst.blast_hyp_subst_tac
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1021
  val claset = Classical.claset
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1022
  val rep_cs = Classical.rep_cs
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1023
  val cla_modifiers = Classical.cla_modifiers
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1024
  val cla_meth' = Classical.cla_meth'
25388
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
  1025
);
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1026
val Blast_tac = Blast.Blast_tac;
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1027
val blast_tac = Blast.blast_tac;
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1028
*}
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1029
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1030
setup Blast.setup
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1031
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1032
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1033
subsubsection {* Simplifier *}
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1034
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1035
lemma eta_contract_eq: "(%s. f s) = f" ..
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1036
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1037
lemma simp_thms:
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
  1038
  shows not_not: "(~ ~ P) = P"
15354
9234f5765d9c Added > and >= sugar
nipkow
parents: 15288
diff changeset
  1039
  and Not_eq_iff: "((~P) = (~Q)) = (P = Q)"
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
  1040
  and
12436
a2df07fefed7 Replaced several occurrences of "blast" by "rules".
berghofe
parents: 12386
diff changeset
  1041
    "(P ~= Q) = (P = (~Q))"
a2df07fefed7 Replaced several occurrences of "blast" by "rules".
berghofe
parents: 12386
diff changeset
  1042
    "(P | ~P) = True"    "(~P | P) = True"
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1043
    "(x = x) = True"
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1044
  and not_True_eq_False: "(\<not> True) = False"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1045
  and not_False_eq_True: "(\<not> False) = True"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1046
  and
12436
a2df07fefed7 Replaced several occurrences of "blast" by "rules".
berghofe
parents: 12386
diff changeset
  1047
    "(~P) ~= P"  "P ~= (~P)"
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1048
    "(True=P) = P"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1049
  and eq_True: "(P = True) = P"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1050
  and "(False=P) = (~P)"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1051
  and eq_False: "(P = False) = (\<not> P)"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1052
  and
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1053
    "(True --> P) = P"  "(False --> P) = True"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1054
    "(P --> True) = True"  "(P --> P) = True"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1055
    "(P --> False) = (~P)"  "(P --> ~P) = (~P)"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1056
    "(P & True) = P"  "(True & P) = P"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1057
    "(P & False) = False"  "(False & P) = False"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1058
    "(P & P) = P"  "(P & (P & Q)) = (P & Q)"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1059
    "(P & ~P) = False"    "(~P & P) = False"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1060
    "(P | True) = True"  "(True | P) = True"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1061
    "(P | False) = P"  "(False | P) = P"
12436
a2df07fefed7 Replaced several occurrences of "blast" by "rules".
berghofe
parents: 12386
diff changeset
  1062
    "(P | P) = P"  "(P | (P | Q)) = (P | Q)" and
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1063
    "(ALL x. P) = P"  "(EX x. P) = P"  "EX x. x=t"  "EX x. t=x"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1064
    -- {* needed for the one-point-rule quantifier simplification procs *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1065
    -- {* essential for termination!! *} and
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1066
    "!!P. (EX x. x=t & P(x)) = P(t)"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1067
    "!!P. (EX x. t=x & P(x)) = P(t)"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1068
    "!!P. (ALL x. x=t --> P(x)) = P(t)"
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
  1069
    "!!P. (ALL x. t=x --> P(x)) = P(t)"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1070
  by (blast, blast, blast, blast, blast, iprover+)
13421
8fcdf4a26468 simplified locale predicates;
wenzelm
parents: 13412
diff changeset
  1071
14201
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1072
lemma disj_absorb: "(A | A) = A"
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1073
  by blast
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1074
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1075
lemma disj_left_absorb: "(A | (A | B)) = (A | B)"
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1076
  by blast
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1077
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1078
lemma conj_absorb: "(A & A) = A"
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1079
  by blast
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1080
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1081
lemma conj_left_absorb: "(A & (A & B)) = (A & B)"
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1082
  by blast
7ad7ab89c402 some basic new lemmas
paulson
parents: 13764
diff changeset
  1083
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1084
lemma eq_ac:
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
  1085
  shows eq_commute: "(a=b) = (b=a)"
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
  1086
    and eq_left_commute: "(P=(Q=R)) = (Q=(P=R))"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1087
    and eq_assoc: "((P=Q)=R) = (P=(Q=R))" by (iprover, blast+)
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1088
lemma neq_commute: "(a~=b) = (b~=a)" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1089
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1090
lemma conj_comms:
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
  1091
  shows conj_commute: "(P&Q) = (Q&P)"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1092
    and conj_left_commute: "(P&(Q&R)) = (Q&(P&R))" by iprover+
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1093
lemma conj_assoc: "((P&Q)&R) = (P&(Q&R))" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1094
19174
df9de25e87b3 moved the "use" directive
paulson
parents: 19162
diff changeset
  1095
lemmas conj_ac = conj_commute conj_left_commute conj_assoc
df9de25e87b3 moved the "use" directive
paulson
parents: 19162
diff changeset
  1096
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1097
lemma disj_comms:
12937
0c4fd7529467 clarified syntax of ``long'' statements: fixes/assumes/shows;
wenzelm
parents: 12892
diff changeset
  1098
  shows disj_commute: "(P|Q) = (Q|P)"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1099
    and disj_left_commute: "(P|(Q|R)) = (Q|(P|R))" by iprover+
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1100
lemma disj_assoc: "((P|Q)|R) = (P|(Q|R))" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1101
19174
df9de25e87b3 moved the "use" directive
paulson
parents: 19162
diff changeset
  1102
lemmas disj_ac = disj_commute disj_left_commute disj_assoc
df9de25e87b3 moved the "use" directive
paulson
parents: 19162
diff changeset
  1103
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1104
lemma conj_disj_distribL: "(P&(Q|R)) = (P&Q | P&R)" by iprover
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1105
lemma conj_disj_distribR: "((P|Q)&R) = (P&R | Q&R)" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1106
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1107
lemma disj_conj_distribL: "(P|(Q&R)) = ((P|Q) & (P|R))" by iprover
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1108
lemma disj_conj_distribR: "((P&Q)|R) = ((P|R) & (Q|R))" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1109
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1110
lemma imp_conjR: "(P --> (Q&R)) = ((P-->Q) & (P-->R))" by iprover
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1111
lemma imp_conjL: "((P&Q) -->R)  = (P --> (Q --> R))" by iprover
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1112
lemma imp_disjL: "((P|Q) --> R) = ((P-->R)&(Q-->R))" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1113
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1114
text {* These two are specialized, but @{text imp_disj_not1} is useful in @{text "Auth/Yahalom"}. *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1115
lemma imp_disj_not1: "(P --> Q | R) = (~Q --> P --> R)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1116
lemma imp_disj_not2: "(P --> Q | R) = (~R --> P --> Q)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1117
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1118
lemma imp_disj1: "((P-->Q)|R) = (P--> Q|R)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1119
lemma imp_disj2: "(Q|(P-->R)) = (P--> Q|R)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1120
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1121
lemma imp_cong: "(P = P') ==> (P' ==> (Q = Q')) ==> ((P --> Q) = (P' --> Q'))"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1122
  by iprover
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1123
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1124
lemma de_Morgan_disj: "(~(P | Q)) = (~P & ~Q)" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1125
lemma de_Morgan_conj: "(~(P & Q)) = (~P | ~Q)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1126
lemma not_imp: "(~(P --> Q)) = (P & ~Q)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1127
lemma not_iff: "(P~=Q) = (P = (~Q))" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1128
lemma disj_not1: "(~P | Q) = (P --> Q)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1129
lemma disj_not2: "(P | ~Q) = (Q --> P)"  -- {* changes orientation :-( *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1130
  by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1131
lemma imp_conv_disj: "(P --> Q) = ((~P) | Q)" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1132
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1133
lemma iff_conv_conj_imp: "(P = Q) = ((P --> Q) & (Q --> P))" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1134
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1135
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1136
lemma cases_simp: "((P --> Q) & (~P --> Q)) = Q"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1137
  -- {* Avoids duplication of subgoals after @{text split_if}, when the true and false *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1138
  -- {* cases boil down to the same thing. *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1139
  by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1140
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1141
lemma not_all: "(~ (! x. P(x))) = (? x.~P(x))" by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1142
lemma imp_all: "((! x. P x) --> Q) = (? x. P x --> Q)" by blast
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1143
lemma not_ex: "(~ (? x. P(x))) = (! x.~P(x))" by iprover
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1144
lemma imp_ex: "((? x. P x) --> Q) = (! x. P x --> Q)" by iprover
23403
9e1edc15ef52 added Theorem all_not_ex
chaieb
parents: 23389
diff changeset
  1145
lemma all_not_ex: "(ALL x. P x) = (~ (EX x. ~ P x ))" by blast
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1146
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24280
diff changeset
  1147
declare All_def [noatp]
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24280
diff changeset
  1148
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1149
lemma ex_disj_distrib: "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))" by iprover
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1150
lemma all_conj_distrib: "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))" by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1151
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1152
text {*
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1153
  \medskip The @{text "&"} congruence rule: not included by default!
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1154
  May slow rewrite proofs down by as much as 50\% *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1155
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1156
lemma conj_cong:
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1157
    "(P = P') ==> (P' ==> (Q = Q')) ==> ((P & Q) = (P' & Q'))"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1158
  by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1159
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1160
lemma rev_conj_cong:
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1161
    "(Q = Q') ==> (Q' ==> (P = P')) ==> ((P & Q) = (P' & Q'))"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1162
  by iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1163
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1164
text {* The @{text "|"} congruence rule: not included by default! *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1165
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1166
lemma disj_cong:
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1167
    "(P = P') ==> (~P' ==> (Q = Q')) ==> ((P | Q) = (P' | Q'))"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1168
  by blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1169
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1170
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1171
text {* \medskip if-then-else rules *}
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1172
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1173
lemma if_True: "(if True then x else y) = x"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1174
  by (unfold if_def) blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1175
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1176
lemma if_False: "(if False then x else y) = y"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1177
  by (unfold if_def) blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1178
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1179
lemma if_P: "P ==> (if P then x else y) = x"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1180
  by (unfold if_def) blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1181
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1182
lemma if_not_P: "~P ==> (if P then x else y) = y"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1183
  by (unfold if_def) blast
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1184
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1185
lemma split_if: "P (if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))"
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1186
  apply (rule case_split [of Q])
15481
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15423
diff changeset
  1187
   apply (simplesubst if_P)
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15423
diff changeset
  1188
    prefer 3 apply (simplesubst if_not_P, blast+)
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1189
  done
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1190
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1191
lemma split_if_asm: "P (if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))"
15481
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15423
diff changeset
  1192
by (simplesubst split_if, blast)
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1193
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24280
diff changeset
  1194
lemmas if_splits [noatp] = split_if split_if_asm
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1195
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1196
lemma if_cancel: "(if c then x else x) = x"
15481
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15423
diff changeset
  1197
by (simplesubst split_if, blast)
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1198
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1199
lemma if_eq_cancel: "(if x = y then y else x) = x"
15481
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15423
diff changeset
  1200
by (simplesubst split_if, blast)
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1201
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1202
lemma if_bool_eq_conj: "(if P then Q else R) = ((P-->Q) & (~P-->R))"
19796
d86e7b1fc472 quoted "if";
wenzelm
parents: 19656
diff changeset
  1203
  -- {* This form is useful for expanding @{text "if"}s on the RIGHT of the @{text "==>"} symbol. *}
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1204
  by (rule split_if)
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1205
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1206
lemma if_bool_eq_disj: "(if P then Q else R) = ((P&Q) | (~P&R))"
19796
d86e7b1fc472 quoted "if";
wenzelm
parents: 19656
diff changeset
  1207
  -- {* And this form is useful for expanding @{text "if"}s on the LEFT. *}
15481
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15423
diff changeset
  1208
  apply (simplesubst split_if, blast)
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1209
  done
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1210
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1211
lemma Eq_TrueI: "P ==> P == True" by (unfold atomize_eq) iprover
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1212
lemma Eq_FalseI: "~P ==> P == False" by (unfold atomize_eq) iprover
12281
3bd113b8f7a6 converted simp lemmas;
wenzelm
parents: 12256
diff changeset
  1213
15423
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1214
text {* \medskip let rules for simproc *}
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1215
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1216
lemma Let_folded: "f x \<equiv> g x \<Longrightarrow>  Let x f \<equiv> Let x g"
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1217
  by (unfold Let_def)
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1218
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1219
lemma Let_unfold: "f x \<equiv> g \<Longrightarrow>  Let x f \<equiv> g"
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1220
  by (unfold Let_def)
761a4f8e6ad6 added simproc for Let
schirmer
parents: 15411
diff changeset
  1221
16633
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1222
text {*
16999
307b2ec590ff Turned simp_implies into binary operator.
ballarin
parents: 16775
diff changeset
  1223
  The following copy of the implication operator is useful for
307b2ec590ff Turned simp_implies into binary operator.
ballarin
parents: 16775
diff changeset
  1224
  fine-tuning congruence rules.  It instructs the simplifier to simplify
307b2ec590ff Turned simp_implies into binary operator.
ballarin
parents: 16775
diff changeset
  1225
  its premise.
16633
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1226
*}
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1227
17197
917c6e7ca28d simp_implies: proper named infix;
wenzelm
parents: 16999
diff changeset
  1228
constdefs
917c6e7ca28d simp_implies: proper named infix;
wenzelm
parents: 16999
diff changeset
  1229
  simp_implies :: "[prop, prop] => prop"  (infixr "=simp=>" 1)
28562
4e74209f113e `code func` now just `code`
haftmann
parents: 28513
diff changeset
  1230
  [code del]: "simp_implies \<equiv> op ==>"
16633
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1231
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1232
lemma simp_impliesI:
16633
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1233
  assumes PQ: "(PROP P \<Longrightarrow> PROP Q)"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1234
  shows "PROP P =simp=> PROP Q"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1235
  apply (unfold simp_implies_def)
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1236
  apply (rule PQ)
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1237
  apply assumption
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1238
  done
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1239
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1240
lemma simp_impliesE:
25388
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
  1241
  assumes PQ: "PROP P =simp=> PROP Q"
16633
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1242
  and P: "PROP P"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1243
  and QR: "PROP Q \<Longrightarrow> PROP R"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1244
  shows "PROP R"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1245
  apply (rule QR)
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1246
  apply (rule PQ [unfolded simp_implies_def])
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1247
  apply (rule P)
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1248
  done
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1249
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1250
lemma simp_implies_cong:
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1251
  assumes PP' :"PROP P == PROP P'"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1252
  and P'QQ': "PROP P' ==> (PROP Q == PROP Q')"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1253
  shows "(PROP P =simp=> PROP Q) == (PROP P' =simp=> PROP Q')"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1254
proof (unfold simp_implies_def, rule equal_intr_rule)
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1255
  assume PQ: "PROP P \<Longrightarrow> PROP Q"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1256
  and P': "PROP P'"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1257
  from PP' [symmetric] and P' have "PROP P"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1258
    by (rule equal_elim_rule1)
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1259
  then have "PROP Q" by (rule PQ)
16633
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1260
  with P'QQ' [OF P'] show "PROP Q'" by (rule equal_elim_rule1)
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1261
next
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1262
  assume P'Q': "PROP P' \<Longrightarrow> PROP Q'"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1263
  and P: "PROP P"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1264
  from PP' and P have P': "PROP P'" by (rule equal_elim_rule1)
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1265
  then have "PROP Q'" by (rule P'Q')
16633
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1266
  with P'QQ' [OF P', symmetric] show "PROP Q"
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1267
    by (rule equal_elim_rule1)
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1268
qed
208ebc9311f2 Implemented trick (due to Tobias Nipkow) for fine-tuning simplification
berghofe
parents: 16587
diff changeset
  1269
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1270
lemma uncurry:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1271
  assumes "P \<longrightarrow> Q \<longrightarrow> R"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1272
  shows "P \<and> Q \<longrightarrow> R"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1273
  using assms by blast
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1274
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1275
lemma iff_allI:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1276
  assumes "\<And>x. P x = Q x"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1277
  shows "(\<forall>x. P x) = (\<forall>x. Q x)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1278
  using assms by blast
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1279
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1280
lemma iff_exI:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1281
  assumes "\<And>x. P x = Q x"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1282
  shows "(\<exists>x. P x) = (\<exists>x. Q x)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1283
  using assms by blast
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1284
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1285
lemma all_comm:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1286
  "(\<forall>x y. P x y) = (\<forall>y x. P x y)"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1287
  by blast
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1288
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1289
lemma ex_comm:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1290
  "(\<exists>x y. P x y) = (\<exists>y x. P x y)"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1291
  by blast
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1292
28952
15a4b2cf8c34 made repository layout more coherent with logical distribution structure; stripped some $Id$s
haftmann
parents: 28856
diff changeset
  1293
use "Tools/simpdata.ML"
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1294
ML {* open Simpdata *}
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1295
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1296
setup {*
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1297
  Simplifier.method_setup Splitter.split_modifiers
26496
49ae9456eba9 purely functional setup of claset/simpset/clasimpset;
wenzelm
parents: 26411
diff changeset
  1298
  #> Simplifier.map_simpset (K Simpdata.simpset_simprocs)
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1299
  #> Splitter.setup
26496
49ae9456eba9 purely functional setup of claset/simpset/clasimpset;
wenzelm
parents: 26411
diff changeset
  1300
  #> clasimp_setup
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1301
  #> EqSubst.setup
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1302
*}
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1303
24035
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1304
text {* Simproc for proving @{text "(y = x) == False"} from premise @{text "~(x = y)"}: *}
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1305
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1306
simproc_setup neq ("x = y") = {* fn _ =>
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1307
let
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1308
  val neq_to_EQ_False = @{thm not_sym} RS @{thm Eq_FalseI};
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1309
  fun is_neq eq lhs rhs thm =
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1310
    (case Thm.prop_of thm of
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1311
      _ $ (Not $ (eq' $ l' $ r')) =>
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1312
        Not = HOLogic.Not andalso eq' = eq andalso
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1313
        r' aconv lhs andalso l' aconv rhs
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1314
    | _ => false);
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1315
  fun proc ss ct =
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1316
    (case Thm.term_of ct of
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1317
      eq $ lhs $ rhs =>
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1318
        (case find_first (is_neq eq lhs rhs) (Simplifier.prems_of_ss ss) of
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1319
          SOME thm => SOME (thm RS neq_to_EQ_False)
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1320
        | NONE => NONE)
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1321
     | _ => NONE);
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1322
in proc end;
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1323
*}
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1324
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1325
simproc_setup let_simp ("Let x f") = {*
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1326
let
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1327
  val (f_Let_unfold, x_Let_unfold) =
28741
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1328
    let val [(_ $ (f $ x) $ _)] = prems_of @{thm Let_unfold}
24035
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1329
    in (cterm_of @{theory} f, cterm_of @{theory} x) end
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1330
  val (f_Let_folded, x_Let_folded) =
28741
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1331
    let val [(_ $ (f $ x) $ _)] = prems_of @{thm Let_folded}
24035
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1332
    in (cterm_of @{theory} f, cterm_of @{theory} x) end;
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1333
  val g_Let_folded =
28741
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1334
    let val [(_ $ _ $ (g $ _))] = prems_of @{thm Let_folded}
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1335
    in cterm_of @{theory} g end;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1336
  fun count_loose (Bound i) k = if i >= k then 1 else 0
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1337
    | count_loose (s $ t) k = count_loose s k + count_loose t k
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1338
    | count_loose (Abs (_, _, t)) k = count_loose  t (k + 1)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1339
    | count_loose _ _ = 0;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1340
  fun is_trivial_let (Const (@{const_name Let}, _) $ x $ t) =
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1341
   case t
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1342
    of Abs (_, _, t') => count_loose t' 0 <= 1
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1343
     | _ => true;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1344
in fn _ => fn ss => fn ct => if is_trivial_let (Thm.term_of ct)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1345
  then SOME @{thm Let_def} (*no or one ocurrenc of bound variable*)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1346
  else let (*Norbert Schirmer's case*)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1347
    val ctxt = Simplifier.the_context ss;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1348
    val thy = ProofContext.theory_of ctxt;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1349
    val t = Thm.term_of ct;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1350
    val ([t'], ctxt') = Variable.import_terms false [t] ctxt;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1351
  in Option.map (hd o Variable.export ctxt' ctxt o single)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1352
    (case t' of Const (@{const_name Let},_) $ x $ f => (* x and f are already in normal form *)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1353
      if is_Free x orelse is_Bound x orelse is_Const x
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1354
      then SOME @{thm Let_def}
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1355
      else
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1356
        let
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1357
          val n = case f of (Abs (x, _, _)) => x | _ => "x";
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1358
          val cx = cterm_of thy x;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1359
          val {T = xT, ...} = rep_cterm cx;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1360
          val cf = cterm_of thy f;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1361
          val fx_g = Simplifier.rewrite ss (Thm.capply cf cx);
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1362
          val (_ $ _ $ g) = prop_of fx_g;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1363
          val g' = abstract_over (x,g);
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1364
        in (if (g aconv g')
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1365
             then
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1366
                let
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1367
                  val rl =
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1368
                    cterm_instantiate [(f_Let_unfold, cf), (x_Let_unfold, cx)] @{thm Let_unfold};
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1369
                in SOME (rl OF [fx_g]) end
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1370
             else if Term.betapply (f, x) aconv g then NONE (*avoid identity conversion*)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1371
             else let
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1372
                   val abs_g'= Abs (n,xT,g');
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1373
                   val g'x = abs_g'$x;
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1374
                   val g_g'x = symmetric (beta_conversion false (cterm_of thy g'x));
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1375
                   val rl = cterm_instantiate
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1376
                             [(f_Let_folded, cterm_of thy f), (x_Let_folded, cx),
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1377
                              (g_Let_folded, cterm_of thy abs_g')]
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1378
                             @{thm Let_folded};
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1379
                 in SOME (rl OF [transitive fx_g g_g'x])
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1380
                 end)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1381
        end
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1382
    | _ => NONE)
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1383
  end
1b257449f804 simproc for let
haftmann
parents: 28699
diff changeset
  1384
end *}
24035
74c032aea9ed simplified ResAtpset via NamedThmsFun;
wenzelm
parents: 23948
diff changeset
  1385
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1386
lemma True_implies_equals: "(True \<Longrightarrow> PROP P) \<equiv> PROP P"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1387
proof
23389
aaca6a8e5414 tuned proofs: avoid implicit prems;
wenzelm
parents: 23263
diff changeset
  1388
  assume "True \<Longrightarrow> PROP P"
aaca6a8e5414 tuned proofs: avoid implicit prems;
wenzelm
parents: 23263
diff changeset
  1389
  from this [OF TrueI] show "PROP P" .
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1390
next
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1391
  assume "PROP P"
23389
aaca6a8e5414 tuned proofs: avoid implicit prems;
wenzelm
parents: 23263
diff changeset
  1392
  then show "PROP P" .
21151
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1393
qed
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1394
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1395
lemma ex_simps:
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1396
  "!!P Q. (EX x. P x & Q)   = ((EX x. P x) & Q)"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1397
  "!!P Q. (EX x. P & Q x)   = (P & (EX x. Q x))"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1398
  "!!P Q. (EX x. P x | Q)   = ((EX x. P x) | Q)"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1399
  "!!P Q. (EX x. P | Q x)   = (P | (EX x. Q x))"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1400
  "!!P Q. (EX x. P x --> Q) = ((ALL x. P x) --> Q)"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1401
  "!!P Q. (EX x. P --> Q x) = (P --> (EX x. Q x))"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1402
  -- {* Miniscoping: pushing in existential quantifiers. *}
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1403
  by (iprover | blast)+
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1404
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1405
lemma all_simps:
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1406
  "!!P Q. (ALL x. P x & Q)   = ((ALL x. P x) & Q)"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1407
  "!!P Q. (ALL x. P & Q x)   = (P & (ALL x. Q x))"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1408
  "!!P Q. (ALL x. P x | Q)   = ((ALL x. P x) | Q)"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1409
  "!!P Q. (ALL x. P | Q x)   = (P | (ALL x. Q x))"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1410
  "!!P Q. (ALL x. P x --> Q) = ((EX x. P x) --> Q)"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1411
  "!!P Q. (ALL x. P --> Q x) = (P --> (ALL x. Q x))"
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1412
  -- {* Miniscoping: pushing in universal quantifiers. *}
25bd46916c12 simplified reasoning tools setup
haftmann
parents: 21112
diff changeset
  1413
  by (iprover | blast)+
15481
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15423
diff changeset
  1414
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1415
lemmas [simp] =
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1416
  triv_forall_equality (*prunes params*)
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1417
  True_implies_equals  (*prune asms `True'*)
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1418
  if_True
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1419
  if_False
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1420
  if_cancel
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1421
  if_eq_cancel
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1422
  imp_disjL
20973
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
  1423
  (*In general it seems wrong to add distributive laws by default: they
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
  1424
    might cause exponential blow-up.  But imp_disjL has been in for a while
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
  1425
    and cannot be removed without affecting existing proofs.  Moreover,
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
  1426
    rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
  1427
    grounds that it allows simplification of R in the two cases.*)
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1428
  conj_assoc
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1429
  disj_assoc
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1430
  de_Morgan_conj
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1431
  de_Morgan_disj
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1432
  imp_disj1
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1433
  imp_disj2
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1434
  not_imp
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1435
  disj_not1
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1436
  not_all
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1437
  not_ex
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1438
  cases_simp
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1439
  the_eq_trivial
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1440
  the_sym_eq_trivial
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1441
  ex_simps
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1442
  all_simps
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1443
  simp_thms
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1444
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1445
lemmas [cong] = imp_cong simp_implies_cong
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1446
lemmas [split] = split_if
20973
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
  1447
22377
61610b1beedf tuned ML setup;
wenzelm
parents: 22218
diff changeset
  1448
ML {* val HOL_ss = @{simpset} *}
20973
0b8e436ed071 cleaned up HOL bootstrap
haftmann
parents: 20944
diff changeset
  1449
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1450
text {* Simplifies x assuming c and y assuming ~c *}
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1451
lemma if_cong:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1452
  assumes "b = c"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1453
      and "c \<Longrightarrow> x = u"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1454
      and "\<not> c \<Longrightarrow> y = v"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1455
  shows "(if b then x else y) = (if c then u else v)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1456
  unfolding if_def using assms by simp
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1457
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1458
text {* Prevents simplification of x and y:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1459
  faster and allows the execution of functional programs. *}
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1460
lemma if_weak_cong [cong]:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1461
  assumes "b = c"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1462
  shows "(if b then x else y) = (if c then x else y)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1463
  using assms by (rule arg_cong)
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1464
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1465
text {* Prevents simplification of t: much faster *}
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1466
lemma let_weak_cong:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1467
  assumes "a = b"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1468
  shows "(let x = a in t x) = (let x = b in t x)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1469
  using assms by (rule arg_cong)
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1470
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1471
text {* To tidy up the result of a simproc.  Only the RHS will be simplified. *}
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1472
lemma eq_cong2:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1473
  assumes "u = u'"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1474
  shows "(t \<equiv> u) \<equiv> (t \<equiv> u')"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1475
  using assms by simp
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1476
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1477
lemma if_distrib:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1478
  "f (if c then x else y) = (if c then f x else f y)"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1479
  by simp
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1480
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1481
text {* This lemma restricts the effect of the rewrite rule u=v to the left-hand
21502
7f3ea2b3bab6 prefer antiquotations over LaTeX macros;
wenzelm
parents: 21486
diff changeset
  1482
  side of an equality.  Used in @{text "{Integ,Real}/simproc.ML"} *}
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1483
lemma restrict_to_left:
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1484
  assumes "x = y"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1485
  shows "(x = z) = (y = z)"
23553
af8ae54238f5 use hologic.ML in basic HOL context;
wenzelm
parents: 23530
diff changeset
  1486
  using assms by simp
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1487
17459
9a3925c07392 added code generator setup (from Main.thy);
wenzelm
parents: 17404
diff changeset
  1488
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1489
subsubsection {* Generic cases and induction *}
17459
9a3925c07392 added code generator setup (from Main.thy);
wenzelm
parents: 17404
diff changeset
  1490
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1491
text {* Rule projections: *}
18887
6ad81e3fa478 Added "evaluation" method and oracle.
berghofe
parents: 18867
diff changeset
  1492
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1493
ML {*
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1494
structure ProjectRule = ProjectRuleFun
25388
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
  1495
(
27126
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1496
  val conjunct1 = @{thm conjunct1}
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1497
  val conjunct2 = @{thm conjunct2}
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1498
  val mp = @{thm mp}
25388
5cd130251825 tuned specifications of 'notation';
wenzelm
parents: 25297
diff changeset
  1499
)
17459
9a3925c07392 added code generator setup (from Main.thy);
wenzelm
parents: 17404
diff changeset
  1500
*}
9a3925c07392 added code generator setup (from Main.thy);
wenzelm
parents: 17404
diff changeset
  1501
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1502
constdefs
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1503
  induct_forall where "induct_forall P == \<forall>x. P x"
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1504
  induct_implies where "induct_implies A B == A \<longrightarrow> B"
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1505
  induct_equal where "induct_equal x y == x = y"
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1506
  induct_conj where "induct_conj A B == A \<and> B"
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1507
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1508
lemma induct_forall_eq: "(!!x. P x) == Trueprop (induct_forall (\<lambda>x. P x))"
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1509
  by (unfold atomize_all induct_forall_def)
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1510
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1511
lemma induct_implies_eq: "(A ==> B) == Trueprop (induct_implies A B)"
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1512
  by (unfold atomize_imp induct_implies_def)
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1513
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1514
lemma induct_equal_eq: "(x == y) == Trueprop (induct_equal x y)"
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1515
  by (unfold atomize_eq induct_equal_def)
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1516
28856
5e009a80fe6d Pure syntax: more coherent treatment of aprop, permanent TERM and &&&;
wenzelm
parents: 28741
diff changeset
  1517
lemma induct_conj_eq: "(A &&& B) == Trueprop (induct_conj A B)"
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1518
  by (unfold atomize_conj induct_conj_def)
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1519
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1520
lemmas induct_atomize = induct_forall_eq induct_implies_eq induct_equal_eq induct_conj_eq
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1521
lemmas induct_rulify [symmetric, standard] = induct_atomize
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1522
lemmas induct_rulify_fallback =
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1523
  induct_forall_def induct_implies_def induct_equal_def induct_conj_def
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1524
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1525
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1526
lemma induct_forall_conj: "induct_forall (\<lambda>x. induct_conj (A x) (B x)) =
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1527
    induct_conj (induct_forall A) (induct_forall B)"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1528
  by (unfold induct_forall_def induct_conj_def) iprover
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1529
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1530
lemma induct_implies_conj: "induct_implies C (induct_conj A B) =
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1531
    induct_conj (induct_implies C A) (induct_implies C B)"
17589
58eeffd73be1 renamed rules to iprover
nipkow
parents: 17459
diff changeset
  1532
  by (unfold induct_implies_def induct_conj_def) iprover
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1533
13598
8bc77b17f59f Fixed problem with induct_conj_curry: variable C should have type prop.
berghofe
parents: 13596
diff changeset
  1534
lemma induct_conj_curry: "(induct_conj A B ==> PROP C) == (A ==> B ==> PROP C)"
8bc77b17f59f Fixed problem with induct_conj_curry: variable C should have type prop.
berghofe
parents: 13596
diff changeset
  1535
proof
8bc77b17f59f Fixed problem with induct_conj_curry: variable C should have type prop.
berghofe
parents: 13596
diff changeset
  1536
  assume r: "induct_conj A B ==> PROP C" and A B
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1537
  show "PROP C" by (rule r) (simp add: induct_conj_def `A` `B`)
13598
8bc77b17f59f Fixed problem with induct_conj_curry: variable C should have type prop.
berghofe
parents: 13596
diff changeset
  1538
next
8bc77b17f59f Fixed problem with induct_conj_curry: variable C should have type prop.
berghofe
parents: 13596
diff changeset
  1539
  assume r: "A ==> B ==> PROP C" and "induct_conj A B"
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1540
  show "PROP C" by (rule r) (simp_all add: `induct_conj A B` [unfolded induct_conj_def])
13598
8bc77b17f59f Fixed problem with induct_conj_curry: variable C should have type prop.
berghofe
parents: 13596
diff changeset
  1541
qed
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1542
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1543
lemmas induct_conj = induct_forall_conj induct_implies_conj induct_conj_curry
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1544
11989
d4bcba4e080e renamed inductive_XXX to induct_XXX;
wenzelm
parents: 11977
diff changeset
  1545
hide const induct_forall induct_implies induct_equal induct_conj
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1546
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1547
text {* Method setup. *}
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1548
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1549
ML {*
27126
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1550
structure Induct = InductFun
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1551
(
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1552
  val cases_default = @{thm case_split}
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1553
  val atomize = @{thms induct_atomize}
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1554
  val rulify = @{thms induct_rulify}
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1555
  val rulify_fallback = @{thms induct_rulify_fallback}
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1556
)
11824
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1557
*}
f4c1882dde2c setup generic cases and induction (from Inductive.thy);
wenzelm
parents: 11770
diff changeset
  1558
24830
a7b3ab44d993 moved Pure/Isar/induct_attrib.ML and Provers/induct_method.ML to Tools/induct.ML;
wenzelm
parents: 24748
diff changeset
  1559
setup Induct.setup
18457
356a9f711899 structure ProjectRule;
wenzelm
parents: 17992
diff changeset
  1560
27326
d3beec370964 moved src/HOL/Tools/induct_tacs.ML to src/Tools/induct_tacs.ML;
wenzelm
parents: 27212
diff changeset
  1561
use "~~/src/Tools/induct_tacs.ML"
27126
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1562
setup InductTacs.setup
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1563
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1564
28325
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1565
subsubsection {* Coherent logic *}
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1566
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1567
ML {*
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1568
structure Coherent = CoherentFun
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1569
(
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1570
  val atomize_elimL = @{thm atomize_elimL}
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1571
  val atomize_exL = @{thm atomize_exL}
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1572
  val atomize_conjL = @{thm atomize_conjL}
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1573
  val atomize_disjL = @{thm atomize_disjL}
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1574
  val operator_names =
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1575
    [@{const_name "op |"}, @{const_name "op &"}, @{const_name "Ex"}]
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1576
);
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1577
*}
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1578
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1579
setup Coherent.setup
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1580
0b6b83ec8458 Added setup for coherent logic prover.
berghofe
parents: 28227
diff changeset
  1581
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1582
subsection {* Other simple lemmas and lemma duplicates *}
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1583
24166
7b28dc69bdbb new nbe implementation
haftmann
parents: 24035
diff changeset
  1584
lemma Let_0 [simp]: "Let 0 f = f 0"
7b28dc69bdbb new nbe implementation
haftmann
parents: 24035
diff changeset
  1585
  unfolding Let_def ..
7b28dc69bdbb new nbe implementation
haftmann
parents: 24035
diff changeset
  1586
7b28dc69bdbb new nbe implementation
haftmann
parents: 24035
diff changeset
  1587
lemma Let_1 [simp]: "Let 1 f = f 1"
7b28dc69bdbb new nbe implementation
haftmann
parents: 24035
diff changeset
  1588
  unfolding Let_def ..
7b28dc69bdbb new nbe implementation
haftmann
parents: 24035
diff changeset
  1589
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1590
lemma ex1_eq [iff]: "EX! x. x = t" "EX! x. t = x"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1591
  by blast+
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1592
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1593
lemma choice_eq: "(ALL x. EX! y. P x y) = (EX! f. ALL x. P x (f x))"
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1594
  apply (rule iffI)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1595
  apply (rule_tac a = "%x. THE y. P x y" in ex1I)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1596
  apply (fast dest!: theI')
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1597
  apply (fast intro: ext the1_equality [symmetric])
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1598
  apply (erule ex1E)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1599
  apply (rule allI)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1600
  apply (rule ex1I)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1601
  apply (erule spec)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1602
  apply (erule_tac x = "%z. if z = x then y else f z" in allE)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1603
  apply (erule impE)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1604
  apply (rule allI)
27126
3ede9103de8e eliminated obsolete case_split_thm -- use case_split;
wenzelm
parents: 27107
diff changeset
  1605
  apply (case_tac "xa = x")
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1606
  apply (drule_tac [3] x = x in fun_cong, simp_all)
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1607
  done
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1608
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1609
lemma mk_left_commute:
21547
9c9fdf4c2949 moved order arities for fun and bool to Fun/Orderings
haftmann
parents: 21524
diff changeset
  1610
  fixes f (infix "\<otimes>" 60)
9c9fdf4c2949 moved order arities for fun and bool to Fun/Orderings
haftmann
parents: 21524
diff changeset
  1611
  assumes a: "\<And>x y z. (x \<otimes> y) \<otimes> z = x \<otimes> (y \<otimes> z)" and
9c9fdf4c2949 moved order arities for fun and bool to Fun/Orderings
haftmann
parents: 21524
diff changeset
  1612
          c: "\<And>x y. x \<otimes> y = y \<otimes> x"
9c9fdf4c2949 moved order arities for fun and bool to Fun/Orderings
haftmann
parents: 21524
diff changeset
  1613
  shows "x \<otimes> (y \<otimes> z) = y \<otimes> (x \<otimes> z)"
20944
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1614
  by (rule trans [OF trans [OF c a] arg_cong [OF c, of "f y"]])
34b2c1bb7178 cleanup basic HOL bootstrap
haftmann
parents: 20833
diff changeset
  1615
22218
30a8890d2967 dropped lemma duplicates in HOL.thy
haftmann
parents: 22129
diff changeset
  1616
lemmas eq_sym_conv = eq_commute
30a8890d2967 dropped lemma duplicates in HOL.thy
haftmann
parents: 22129
diff changeset
  1617
23037
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1618
lemma nnf_simps:
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1619
  "(\<not>(P \<and> Q)) = (\<not> P \<or> \<not> Q)" "(\<not> (P \<or> Q)) = (\<not> P \<and> \<not>Q)" "(P \<longrightarrow> Q) = (\<not>P \<or> Q)" 
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1620
  "(P = Q) = ((P \<and> Q) \<or> (\<not>P \<and> \<not> Q))" "(\<not>(P = Q)) = ((P \<and> \<not> Q) \<or> (\<not>P \<and> Q))" 
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1621
  "(\<not> \<not>(P)) = P"
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1622
by blast+
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1623
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1624
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1625
subsection {* Basic ML bindings *}
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1626
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1627
ML {*
22129
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1628
val FalseE = @{thm FalseE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1629
val Let_def = @{thm Let_def}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1630
val TrueI = @{thm TrueI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1631
val allE = @{thm allE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1632
val allI = @{thm allI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1633
val all_dupE = @{thm all_dupE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1634
val arg_cong = @{thm arg_cong}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1635
val box_equals = @{thm box_equals}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1636
val ccontr = @{thm ccontr}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1637
val classical = @{thm classical}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1638
val conjE = @{thm conjE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1639
val conjI = @{thm conjI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1640
val conjunct1 = @{thm conjunct1}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1641
val conjunct2 = @{thm conjunct2}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1642
val disjCI = @{thm disjCI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1643
val disjE = @{thm disjE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1644
val disjI1 = @{thm disjI1}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1645
val disjI2 = @{thm disjI2}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1646
val eq_reflection = @{thm eq_reflection}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1647
val ex1E = @{thm ex1E}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1648
val ex1I = @{thm ex1I}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1649
val ex1_implies_ex = @{thm ex1_implies_ex}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1650
val exE = @{thm exE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1651
val exI = @{thm exI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1652
val excluded_middle = @{thm excluded_middle}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1653
val ext = @{thm ext}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1654
val fun_cong = @{thm fun_cong}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1655
val iffD1 = @{thm iffD1}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1656
val iffD2 = @{thm iffD2}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1657
val iffI = @{thm iffI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1658
val impE = @{thm impE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1659
val impI = @{thm impI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1660
val meta_eq_to_obj_eq = @{thm meta_eq_to_obj_eq}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1661
val mp = @{thm mp}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1662
val notE = @{thm notE}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1663
val notI = @{thm notI}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1664
val not_all = @{thm not_all}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1665
val not_ex = @{thm not_ex}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1666
val not_iff = @{thm not_iff}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1667
val not_not = @{thm not_not}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1668
val not_sym = @{thm not_sym}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1669
val refl = @{thm refl}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1670
val rev_mp = @{thm rev_mp}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1671
val spec = @{thm spec}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1672
val ssubst = @{thm ssubst}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1673
val subst = @{thm subst}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1674
val sym = @{thm sym}
bb2203c93316 tuned ML setup;
wenzelm
parents: 21671
diff changeset
  1675
val trans = @{thm trans}
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1676
*}
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1677
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1678
28400
89904cfd41c3 polished code generator setup
haftmann
parents: 28346
diff changeset
  1679
subsection {* Code generator basics -- see further theory @{text "Code_Setup"} *}
89904cfd41c3 polished code generator setup
haftmann
parents: 28346
diff changeset
  1680
89904cfd41c3 polished code generator setup
haftmann
parents: 28346
diff changeset
  1681
text {* Equality *}
24844
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24842
diff changeset
  1682
29608
564ea783ace8 no base sort in class import
haftmann
parents: 29505
diff changeset
  1683
class eq =
26513
6f306c8c2c54 explicit class "eq" for operational equality
haftmann
parents: 26496
diff changeset
  1684
  fixes eq :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
28400
89904cfd41c3 polished code generator setup
haftmann
parents: 28346
diff changeset
  1685
  assumes eq_equals: "eq x y \<longleftrightarrow> x = y"
26513
6f306c8c2c54 explicit class "eq" for operational equality
haftmann
parents: 26496
diff changeset
  1686
begin
6f306c8c2c54 explicit class "eq" for operational equality
haftmann
parents: 26496
diff changeset
  1687
28346
b8390cd56b8f discontinued special treatment of op = vs. eq_class.eq
haftmann
parents: 28325
diff changeset
  1688
lemma eq: "eq = (op =)"
b8390cd56b8f discontinued special treatment of op = vs. eq_class.eq
haftmann
parents: 28325
diff changeset
  1689
  by (rule ext eq_equals)+
b8390cd56b8f discontinued special treatment of op = vs. eq_class.eq
haftmann
parents: 28325
diff changeset
  1690
b8390cd56b8f discontinued special treatment of op = vs. eq_class.eq
haftmann
parents: 28325
diff changeset
  1691
lemma eq_refl: "eq x x \<longleftrightarrow> True"
b8390cd56b8f discontinued special treatment of op = vs. eq_class.eq
haftmann
parents: 28325
diff changeset
  1692
  unfolding eq by rule+
b8390cd56b8f discontinued special treatment of op = vs. eq_class.eq
haftmann
parents: 28325
diff changeset
  1693
26513
6f306c8c2c54 explicit class "eq" for operational equality
haftmann
parents: 26496
diff changeset
  1694
end
6f306c8c2c54 explicit class "eq" for operational equality
haftmann
parents: 26496
diff changeset
  1695
28513
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1696
text {* Module setup *}
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1697
29505
c6d2d23909d1 added HOL-Base image
haftmann
parents: 29105
diff changeset
  1698
use "Tools/recfun_codegen.ML"
28513
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1699
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1700
setup {*
28663
bd8438543bf2 code identifier namings are no longer imperative
haftmann
parents: 28562
diff changeset
  1701
  Code_ML.setup
28513
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1702
  #> Code_Haskell.setup
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1703
  #> Nbe.setup
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1704
  #> Codegen.setup
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1705
  #> RecfunCodegen.setup
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1706
*}
b0b30fd6c264 re-introduces axiom subst
haftmann
parents: 28400
diff changeset
  1707
23247
b99dce43d252 merged Code_Generator.thy into HOL.thy
haftmann
parents: 23171
diff changeset
  1708
29863
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1709
subsection {* Nitpick theorem store *}
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1710
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1711
ML {*
29866
6e93ae65c678 Added Nitpick_Const_Psimp attribute, dropped the 's' in Nitpick_Const_Simps, and killed the Nitpick_Ind_Intros attribute.
blanchet
parents: 29863
diff changeset
  1712
structure Nitpick_Const_Simp_Thms = NamedThmsFun
29863
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1713
(
29866
6e93ae65c678 Added Nitpick_Const_Psimp attribute, dropped the 's' in Nitpick_Const_Simps, and killed the Nitpick_Ind_Intros attribute.
blanchet
parents: 29863
diff changeset
  1714
  val name = "nitpick_const_simp"
29869
a7a8b90cd882 Renamed descriptions of Nitpick (and ATP) attributes, so that they fit well with the rest of the sentence in ProofGeneral.
blanchet
parents: 29868
diff changeset
  1715
  val description = "equational specification of constants as needed by Nitpick"
29863
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1716
)
29866
6e93ae65c678 Added Nitpick_Const_Psimp attribute, dropped the 's' in Nitpick_Const_Simps, and killed the Nitpick_Ind_Intros attribute.
blanchet
parents: 29863
diff changeset
  1717
structure Nitpick_Const_Psimp_Thms = NamedThmsFun
29863
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1718
(
29866
6e93ae65c678 Added Nitpick_Const_Psimp attribute, dropped the 's' in Nitpick_Const_Simps, and killed the Nitpick_Ind_Intros attribute.
blanchet
parents: 29863
diff changeset
  1719
  val name = "nitpick_const_psimp"
29869
a7a8b90cd882 Renamed descriptions of Nitpick (and ATP) attributes, so that they fit well with the rest of the sentence in ProofGeneral.
blanchet
parents: 29868
diff changeset
  1720
  val description = "partial equational specification of constants as needed by Nitpick"
29863
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1721
)
29868
787349bb53e9 Reintroduced nitpick_ind_intro attribute.
blanchet
parents: 29866
diff changeset
  1722
structure Nitpick_Ind_Intro_Thms = NamedThmsFun
787349bb53e9 Reintroduced nitpick_ind_intro attribute.
blanchet
parents: 29866
diff changeset
  1723
(
787349bb53e9 Reintroduced nitpick_ind_intro attribute.
blanchet
parents: 29866
diff changeset
  1724
  val name = "nitpick_ind_intro"
29869
a7a8b90cd882 Renamed descriptions of Nitpick (and ATP) attributes, so that they fit well with the rest of the sentence in ProofGeneral.
blanchet
parents: 29868
diff changeset
  1725
  val description = "introduction rules for (co)inductive predicates as needed by Nitpick"
29868
787349bb53e9 Reintroduced nitpick_ind_intro attribute.
blanchet
parents: 29866
diff changeset
  1726
)
29863
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1727
*}
29866
6e93ae65c678 Added Nitpick_Const_Psimp attribute, dropped the 's' in Nitpick_Const_Simps, and killed the Nitpick_Ind_Intros attribute.
blanchet
parents: 29863
diff changeset
  1728
setup {* Nitpick_Const_Simp_Thms.setup
29868
787349bb53e9 Reintroduced nitpick_ind_intro attribute.
blanchet
parents: 29866
diff changeset
  1729
         #> Nitpick_Const_Psimp_Thms.setup
787349bb53e9 Reintroduced nitpick_ind_intro attribute.
blanchet
parents: 29866
diff changeset
  1730
         #> Nitpick_Ind_Intro_Thms.setup *}
29863
dadad1831e9d Added "nitpick_const_simps" and "nitpick_ind_intros" attributes for theorems;
blanchet
parents: 29608
diff changeset
  1731
22839
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1732
subsection {* Legacy tactics and ML bindings *}
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1733
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1734
ML {*
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1735
fun strip_tac i = REPEAT (resolve_tac [impI, allI] i);
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1736
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1737
(* combination of (spec RS spec RS ...(j times) ... spec RS mp) *)
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1738
local
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1739
  fun wrong_prem (Const ("All", _) $ (Abs (_, _, t))) = wrong_prem t
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1740
    | wrong_prem (Bound _) = true
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1741
    | wrong_prem _ = false;
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1742
  val filter_right = filter (not o wrong_prem o HOLogic.dest_Trueprop o hd o Thm.prems_of);
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1743
in
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1744
  fun smp i = funpow i (fn m => filter_right ([spec] RL m)) ([mp]);
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1745
  fun smp_tac j = EVERY'[dresolve_tac (smp j), atac];
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1746
end;
22839
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1747
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1748
val all_conj_distrib = thm "all_conj_distrib";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1749
val all_simps = thms "all_simps";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1750
val atomize_not = thm "atomize_not";
24830
a7b3ab44d993 moved Pure/Isar/induct_attrib.ML and Provers/induct_method.ML to Tools/induct.ML;
wenzelm
parents: 24748
diff changeset
  1751
val case_split = thm "case_split";
22839
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1752
val cases_simp = thm "cases_simp";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1753
val choice_eq = thm "choice_eq"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1754
val cong = thm "cong"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1755
val conj_comms = thms "conj_comms";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1756
val conj_cong = thm "conj_cong";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1757
val de_Morgan_conj = thm "de_Morgan_conj";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1758
val de_Morgan_disj = thm "de_Morgan_disj";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1759
val disj_assoc = thm "disj_assoc";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1760
val disj_comms = thms "disj_comms";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1761
val disj_cong = thm "disj_cong";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1762
val eq_ac = thms "eq_ac";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1763
val eq_cong2 = thm "eq_cong2"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1764
val Eq_FalseI = thm "Eq_FalseI";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1765
val Eq_TrueI = thm "Eq_TrueI";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1766
val Ex1_def = thm "Ex1_def"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1767
val ex_disj_distrib = thm "ex_disj_distrib";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1768
val ex_simps = thms "ex_simps";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1769
val if_cancel = thm "if_cancel";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1770
val if_eq_cancel = thm "if_eq_cancel";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1771
val if_False = thm "if_False";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1772
val iff_conv_conj_imp = thm "iff_conv_conj_imp";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1773
val iff = thm "iff"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1774
val if_splits = thms "if_splits";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1775
val if_True = thm "if_True";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1776
val if_weak_cong = thm "if_weak_cong"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1777
val imp_all = thm "imp_all";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1778
val imp_cong = thm "imp_cong";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1779
val imp_conjL = thm "imp_conjL";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1780
val imp_conjR = thm "imp_conjR";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1781
val imp_conv_disj = thm "imp_conv_disj";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1782
val simp_implies_def = thm "simp_implies_def";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1783
val simp_thms = thms "simp_thms";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1784
val split_if = thm "split_if";
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1785
val the1_equality = thm "the1_equality"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1786
val theI = thm "theI"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1787
val theI' = thm "theI'"
ede26eb5e549 dropped HOL.ML
haftmann
parents: 22744
diff changeset
  1788
val True_implies_equals = thm "True_implies_equals";
23037
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1789
val nnf_conv = Simplifier.rewrite (HOL_basic_ss addsimps simp_thms @ @{thms "nnf_simps"})
6c72943a71b1 added a set of NNF normalization lemmas and nnf_conv
chaieb
parents: 22993
diff changeset
  1790
21671
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1791
*}
f7d652ffef09 removed legacy ML bindings;
wenzelm
parents: 21547
diff changeset
  1792
14357
e49d5d5ae66a print translation for ALL x <= n. P x
kleing
parents: 14295
diff changeset
  1793
end