src/FOLP/IFOLP.thy
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(*  Title:      FOLP/IFOLP.thy
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    Author:     Martin D Coen, Cambridge University Computer Laboratory
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    Copyright   1992  University of Cambridge
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*)
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section \<open>Intuitionistic First-Order Logic with Proofs\<close>
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theory IFOLP
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imports Pure
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begin
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ML_file "~~/src/Tools/misc_legacy.ML"
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setup Pure_Thy.old_appl_syntax_setup
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class "term"
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default_sort "term"
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typedecl p
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typedecl o
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consts
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      (*** Judgements ***)
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 Proof          ::   "[o,p]=>prop"
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 EqProof        ::   "[p,p,o]=>prop"    ("(3_ /= _ :/ _)" [10,10,10] 5)
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      (*** Logical Connectives -- Type Formers ***)
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 eq             ::      "['a,'a] => o"  (infixl "=" 50)
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 True           ::      "o"
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 False          ::      "o"
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 Not            ::      "o => o"        ("~ _" [40] 40)
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 conj           ::      "[o,o] => o"    (infixr "&" 35)
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 disj           ::      "[o,o] => o"    (infixr "|" 30)
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 imp            ::      "[o,o] => o"    (infixr "-->" 25)
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 iff            ::      "[o,o] => o"    (infixr "<->" 25)
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      (*Quantifiers*)
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 All            ::      "('a => o) => o"        (binder "ALL " 10)
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 Ex             ::      "('a => o) => o"        (binder "EX " 10)
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 Ex1            ::      "('a => o) => o"        (binder "EX! " 10)
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      (*Rewriting gadgets*)
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 NORM           ::      "o => o"
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 norm           ::      "'a => 'a"
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      (*** Proof Term Formers: precedence must exceed 50 ***)
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 tt             :: "p"
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 contr          :: "p=>p"
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 fst            :: "p=>p"
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 snd            :: "p=>p"
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 pair           :: "[p,p]=>p"           ("(1<_,/_>)")
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 split          :: "[p, [p,p]=>p] =>p"
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 inl            :: "p=>p"
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 inr            :: "p=>p"
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 "when"         :: "[p, p=>p, p=>p]=>p"
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 lambda         :: "(p => p) => p"      (binder "lam " 55)
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 App            :: "[p,p]=>p"           (infixl "`" 60)
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 alll           :: "['a=>p]=>p"         (binder "all " 55)
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 app            :: "[p,'a]=>p"          (infixl "^" 55)
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 exists         :: "['a,p]=>p"          ("(1[_,/_])")
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 xsplit         :: "[p,['a,p]=>p]=>p"
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 ideq           :: "'a=>p"
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 idpeel         :: "[p,'a=>p]=>p"
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 nrm            :: p
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 NRM            :: p
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syntax "_Proof" :: "[p,o]=>prop"    ("(_ /: _)" [51, 10] 5)
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parse_translation \<open>
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  let fun proof_tr [p, P] = Const (@{const_syntax Proof}, dummyT) $ P $ p
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  in [(@{syntax_const "_Proof"}, K proof_tr)] end
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\<close>
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(*show_proofs = true displays the proof terms -- they are ENORMOUS*)
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ML \<open>val show_proofs = Attrib.setup_config_bool @{binding show_proofs} (K false)\<close>
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print_translation \<open>
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  let
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    fun proof_tr' ctxt [P, p] =
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      if Config.get ctxt show_proofs then Const (@{syntax_const "_Proof"}, dummyT) $ p $ P
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      else P
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  in [(@{const_syntax Proof}, proof_tr')] end
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\<close>
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(**** Propositional logic ****)
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(*Equality*)
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(* Like Intensional Equality in MLTT - but proofs distinct from terms *)
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axiomatization where
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ieqI:      "ideq(a) : a=a" and
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ieqE:      "[| p : a=b;  !!x. f(x) : P(x,x) |] ==> idpeel(p,f) : P(a,b)"
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(* Truth and Falsity *)
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axiomatization where
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TrueI:     "tt : True" and
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FalseE:    "a:False ==> contr(a):P"
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(* Conjunction *)
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axiomatization where
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conjI:     "[| a:P;  b:Q |] ==> <a,b> : P&Q" and
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conjunct1: "p:P&Q ==> fst(p):P" and
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conjunct2: "p:P&Q ==> snd(p):Q"
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(* Disjunction *)
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axiomatization where
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disjI1:    "a:P ==> inl(a):P|Q" and
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disjI2:    "b:Q ==> inr(b):P|Q" and
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disjE:     "[| a:P|Q;  !!x. x:P ==> f(x):R;  !!x. x:Q ==> g(x):R
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           |] ==> when(a,f,g):R"
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(* Implication *)
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axiomatization where
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impI:      "\<And>P Q f. (!!x. x:P ==> f(x):Q) ==> lam x. f(x):P-->Q" and
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mp:        "\<And>P Q f. [| f:P-->Q;  a:P |] ==> f`a:Q"
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(*Quantifiers*)
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axiomatization where
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allI:      "\<And>P. (!!x. f(x) : P(x)) ==> all x. f(x) : ALL x. P(x)" and
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spec:      "\<And>P f. (f:ALL x. P(x)) ==> f^x : P(x)"
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axiomatization where
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exI:       "p : P(x) ==> [x,p] : EX x. P(x)" and
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exE:       "[| p: EX x. P(x);  !!x u. u:P(x) ==> f(x,u) : R |] ==> xsplit(p,f):R"
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(**** Equality between proofs ****)
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axiomatization where
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prefl:     "a : P ==> a = a : P" and
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psym:      "a = b : P ==> b = a : P" and
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ptrans:    "[| a = b : P;  b = c : P |] ==> a = c : P"
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axiomatization where
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idpeelB:   "[| !!x. f(x) : P(x,x) |] ==> idpeel(ideq(a),f) = f(a) : P(a,a)"
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axiomatization where
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fstB:      "a:P ==> fst(<a,b>) = a : P" and
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sndB:      "b:Q ==> snd(<a,b>) = b : Q" and
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pairEC:    "p:P&Q ==> p = <fst(p),snd(p)> : P&Q"
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axiomatization where
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whenBinl:  "[| a:P;  !!x. x:P ==> f(x) : Q |] ==> when(inl(a),f,g) = f(a) : Q" and
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whenBinr:  "[| b:P;  !!x. x:P ==> g(x) : Q |] ==> when(inr(b),f,g) = g(b) : Q" and
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plusEC:    "a:P|Q ==> when(a,%x. inl(x),%y. inr(y)) = a : P|Q"
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axiomatization where
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applyB:     "[| a:P;  !!x. x:P ==> b(x) : Q |] ==> (lam x. b(x)) ` a = b(a) : Q" and
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funEC:      "f:P ==> f = lam x. f`x : P"
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axiomatization where
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specB:      "[| !!x. f(x) : P(x) |] ==> (all x. f(x)) ^ a = f(a) : P(a)"
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(**** Definitions ****)
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defs
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not_def:              "~P == P-->False"
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iff_def:         "P<->Q == (P-->Q) & (Q-->P)"
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(*Unique existence*)
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ex1_def:   "EX! x. P(x) == EX x. P(x) & (ALL y. P(y) --> y=x)"
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(*Rewriting -- special constants to flag normalized terms and formulae*)
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axiomatization where
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norm_eq: "nrm : norm(x) = x" and
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NORM_iff:        "NRM : NORM(P) <-> P"
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(*** Sequent-style elimination rules for & --> and ALL ***)
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schematic_goal conjE:
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  assumes "p:P&Q"
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    and "!!x y.[| x:P; y:Q |] ==> f(x,y):R"
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  shows "?a:R"
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  apply (rule assms(2))
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   apply (rule conjunct1 [OF assms(1)])
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  apply (rule conjunct2 [OF assms(1)])
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  done
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schematic_goal impE:
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  assumes "p:P-->Q"
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    and "q:P"
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    and "!!x. x:Q ==> r(x):R"
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  shows "?p:R"
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  apply (rule assms mp)+
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  done
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schematic_goal allE:
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  assumes "p:ALL x. P(x)"
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    and "!!y. y:P(x) ==> q(y):R"
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  shows "?p:R"
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  apply (rule assms spec)+
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  done
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(*Duplicates the quantifier; for use with eresolve_tac*)
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schematic_goal all_dupE:
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  assumes "p:ALL x. P(x)"
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    and "!!y z.[| y:P(x); z:ALL x. P(x) |] ==> q(y,z):R"
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  shows "?p:R"
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  apply (rule assms spec)+
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  done
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(*** Negation rules, which translate between ~P and P-->False ***)
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schematic_goal notI:
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  assumes "!!x. x:P ==> q(x):False"
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  shows "?p:~P"
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  unfolding not_def
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  apply (assumption | rule assms impI)+
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  done
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schematic_goal notE: "p:~P \<Longrightarrow> q:P \<Longrightarrow> ?p:R"
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  unfolding not_def
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  apply (drule (1) mp)
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  apply (erule FalseE)
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  done
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(*This is useful with the special implication rules for each kind of P. *)
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schematic_goal not_to_imp:
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  assumes "p:~P"
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    and "!!x. x:(P-->False) ==> q(x):Q"
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  shows "?p:Q"
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  apply (assumption | rule assms impI notE)+
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  done
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(* For substitution int an assumption P, reduce Q to P-->Q, substitute into
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   this implication, then apply impI to move P back into the assumptions.*)
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schematic_goal rev_mp: "[| p:P;  q:P --> Q |] ==> ?p:Q"
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  apply (assumption | rule mp)+
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  done
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(*Contrapositive of an inference rule*)
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schematic_goal contrapos:
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  assumes major: "p:~Q"
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    and minor: "!!y. y:P==>q(y):Q"
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  shows "?a:~P"
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  apply (rule major [THEN notE, THEN notI])
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  apply (erule minor)
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  done
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(** Unique assumption tactic.
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    Ignores proof objects.
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    Fails unless one assumption is equal and exactly one is unifiable
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**)
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ML \<open>
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local
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  fun discard_proof (Const (@{const_name Proof}, _) $ P $ _) = P;
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in
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fun uniq_assume_tac ctxt =
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  SUBGOAL
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    (fn (prem,i) =>
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      let val hyps = map discard_proof (Logic.strip_assums_hyp prem)
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          and concl = discard_proof (Logic.strip_assums_concl prem)
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      in
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          if exists (fn hyp => hyp aconv concl) hyps
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          then case distinct (op =) (filter (fn hyp => Term.could_unify (hyp, concl)) hyps) of
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                   [_] => assume_tac ctxt i
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                 |  _  => no_tac
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          else no_tac
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      end);
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end;
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\<close>
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(*** Modus Ponens Tactics ***)
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(*Finds P-->Q and P in the assumptions, replaces implication by Q *)
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ML \<open>
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  fun mp_tac ctxt i =
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    eresolve_tac ctxt [@{thm notE}, make_elim @{thm mp}] i  THEN  assume_tac ctxt i
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\<close>
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method_setup mp = \<open>Scan.succeed (SIMPLE_METHOD' o mp_tac)\<close>
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(*Like mp_tac but instantiates no variables*)
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ML \<open>
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  fun int_uniq_mp_tac ctxt i =
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    eresolve_tac ctxt [@{thm notE}, @{thm impE}] i  THEN  uniq_assume_tac ctxt i
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\<close>
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(*** If-and-only-if ***)
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schematic_goal iffI:
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  assumes "!!x. x:P ==> q(x):Q"
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    and "!!x. x:Q ==> r(x):P"
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  shows "?p:P<->Q"
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  unfolding iff_def
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  apply (assumption | rule assms conjI impI)+
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  done
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schematic_goal iffE:
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  assumes "p:P <-> Q"
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    and "!!x y.[| x:P-->Q; y:Q-->P |] ==> q(x,y):R"
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  shows "?p:R"
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  apply (rule conjE)
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   apply (rule assms(1) [unfolded iff_def])
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  apply (rule assms(2))
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   apply assumption+
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  done
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(* Destruct rules for <-> similar to Modus Ponens *)
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schematic_goal iffD1: "[| p:P <-> Q; q:P |] ==> ?p:Q"
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  unfolding iff_def
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  apply (rule conjunct1 [THEN mp], assumption+)
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  done
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schematic_goal iffD2: "[| p:P <-> Q; q:Q |] ==> ?p:P"
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  unfolding iff_def
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  apply (rule conjunct2 [THEN mp], assumption+)
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  done
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schematic_goal iff_refl: "?p:P <-> P"
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  apply (rule iffI)
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   apply assumption+
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  done
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schematic_goal iff_sym: "p:Q <-> P ==> ?p:P <-> Q"
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  apply (erule iffE)
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  apply (rule iffI)
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   apply (erule (1) mp)+
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  done
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wenzelm
parents: 17480
diff changeset
   330
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   331
schematic_goal iff_trans: "[| p:P <-> Q; q:Q<-> R |] ==> ?p:P <-> R"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   332
  apply (rule iffI)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   333
   apply (assumption | erule iffE | erule (1) impE)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   334
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   335
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   336
(*** Unique existence.  NOTE THAT the following 2 quantifications
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   337
   EX!x such that [EX!y such that P(x,y)]     (sequential)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   338
   EX!x,y such that P(x,y)                    (simultaneous)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   339
 do NOT mean the same thing.  The parser treats EX!x y.P(x,y) as sequential.
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   340
***)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   341
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
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diff changeset
   342
schematic_goal ex1I:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   343
  assumes "p:P(a)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   344
    and "!!x u. u:P(x) ==> f(u) : x=a"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   345
  shows "?p:EX! x. P(x)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   346
  unfolding ex1_def
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   347
  apply (assumption | rule assms exI conjI allI impI)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   348
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   349
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   350
schematic_goal ex1E:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   351
  assumes "p:EX! x. P(x)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   352
    and "!!x u v. [| u:P(x);  v:ALL y. P(y) --> y=x |] ==> f(x,u,v):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   353
  shows "?a : R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   354
  apply (insert assms(1) [unfolded ex1_def])
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   355
  apply (erule exE conjE | assumption | rule assms(1))+
29305
76af2a3c9d28 fixed assumption proof;
wenzelm
parents: 29269
diff changeset
   356
  apply (erule assms(2), assumption)
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   357
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   358
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   359
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   360
(*** <-> congruence rules for simplification ***)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   361
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   362
(*Use iffE on a premise.  For conj_cong, imp_cong, all_cong, ex_cong*)
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   363
ML \<open>
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   364
fun iff_tac ctxt prems i =
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   365
    resolve_tac ctxt (prems RL [@{thm iffE}]) i THEN
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   366
    REPEAT1 (eresolve_tac ctxt [asm_rl, @{thm mp}] i)
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   367
\<close>
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   368
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   369
method_setup iff =
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   370
  \<open>Attrib.thms >> (fn prems => fn ctxt => SIMPLE_METHOD' (iff_tac ctxt prems))\<close>
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   371
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   372
schematic_goal conj_cong:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   373
  assumes "p:P <-> P'"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   374
    and "!!x. x:P' ==> q(x):Q <-> Q'"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   375
  shows "?p:(P&Q) <-> (P'&Q')"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   376
  apply (insert assms(1))
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   377
  apply (assumption | rule iffI conjI | erule iffE conjE mp | iff assms)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   378
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   379
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   380
schematic_goal disj_cong:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   381
  "[| p:P <-> P'; q:Q <-> Q' |] ==> ?p:(P|Q) <-> (P'|Q')"
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   382
  apply (erule iffE disjE disjI1 disjI2 | assumption | rule iffI | mp)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   383
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   384
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   385
schematic_goal imp_cong:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   386
  assumes "p:P <-> P'"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   387
    and "!!x. x:P' ==> q(x):Q <-> Q'"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   388
  shows "?p:(P-->Q) <-> (P'-->Q')"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   389
  apply (insert assms(1))
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   390
  apply (assumption | rule iffI impI | erule iffE | mp | iff assms)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   391
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   392
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   393
schematic_goal iff_cong:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   394
  "[| p:P <-> P'; q:Q <-> Q' |] ==> ?p:(P<->Q) <-> (P'<->Q')"
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   395
  apply (erule iffE | assumption | rule iffI | mp)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   396
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   397
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   398
schematic_goal not_cong:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   399
  "p:P <-> P' ==> ?p:~P <-> ~P'"
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   400
  apply (assumption | rule iffI notI | mp | erule iffE notE)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   401
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   402
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   403
schematic_goal all_cong:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   404
  assumes "!!x. f(x):P(x) <-> Q(x)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   405
  shows "?p:(ALL x. P(x)) <-> (ALL x. Q(x))"
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   406
  apply (assumption | rule iffI allI | mp | erule allE | iff assms)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   407
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   408
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   409
schematic_goal ex_cong:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   410
  assumes "!!x. f(x):P(x) <-> Q(x)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   411
  shows "?p:(EX x. P(x)) <-> (EX x. Q(x))"
59529
d881f5288d5a proper context and method setup;
wenzelm
parents: 59498
diff changeset
   412
  apply (erule exE | assumption | rule iffI exI | mp | iff assms)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   413
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   414
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   415
(*NOT PROVED
56199
8e8d28ed7529 tuned signature -- rearranged modules;
wenzelm
parents: 55380
diff changeset
   416
ML_Thms.bind_thm ("ex1_cong", prove_goal (the_context ())
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   417
    "(!!x.f(x):P(x) <-> Q(x)) ==> ?p:(EX! x.P(x)) <-> (EX! x.Q(x))"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   418
 (fn prems =>
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   419
  [ (REPEAT   (eresolve_tac [ex1E, spec RS mp] 1 ORELSE ares_tac [iffI,ex1I] 1
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   420
      ORELSE   mp_tac 1
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   421
      ORELSE   iff_tac prems 1)) ]))
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   422
*)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   423
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   424
(*** Equality rules ***)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   425
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   426
lemmas refl = ieqI
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   427
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   428
schematic_goal subst:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   429
  assumes prem1: "p:a=b"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   430
    and prem2: "q:P(a)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   431
  shows "?p : P(b)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   432
  apply (rule prem2 [THEN rev_mp])
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   433
  apply (rule prem1 [THEN ieqE])
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   434
  apply (rule impI)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   435
  apply assumption
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   436
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   437
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   438
schematic_goal sym: "q:a=b ==> ?c:b=a"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   439
  apply (erule subst)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   440
  apply (rule refl)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   441
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   442
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   443
schematic_goal trans: "[| p:a=b;  q:b=c |] ==> ?d:a=c"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   444
  apply (erule (1) subst)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   445
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   446
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   447
(** ~ b=a ==> ~ a=b **)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   448
schematic_goal not_sym: "p:~ b=a ==> ?q:~ a=b"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   449
  apply (erule contrapos)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   450
  apply (erule sym)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   451
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   452
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   453
schematic_goal ssubst: "p:b=a \<Longrightarrow> q:P(a) \<Longrightarrow> ?p:P(b)"
45594
wenzelm
parents: 44121
diff changeset
   454
  apply (drule sym)
wenzelm
parents: 44121
diff changeset
   455
  apply (erule subst)
wenzelm
parents: 44121
diff changeset
   456
  apply assumption
wenzelm
parents: 44121
diff changeset
   457
  done
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   458
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   459
(*A special case of ex1E that would otherwise need quantifier expansion*)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   460
schematic_goal ex1_equalsE: "[| p:EX! x. P(x);  q:P(a);  r:P(b) |] ==> ?d:a=b"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   461
  apply (erule ex1E)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   462
  apply (rule trans)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   463
   apply (rule_tac [2] sym)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   464
   apply (assumption | erule spec [THEN mp])+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   465
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   466
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   467
(** Polymorphic congruence rules **)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   468
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   469
schematic_goal subst_context: "[| p:a=b |]  ==>  ?d:t(a)=t(b)"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   470
  apply (erule ssubst)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   471
  apply (rule refl)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   472
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   473
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   474
schematic_goal subst_context2: "[| p:a=b;  q:c=d |]  ==>  ?p:t(a,c)=t(b,d)"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   475
  apply (erule ssubst)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   476
  apply (rule refl)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   477
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   478
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   479
schematic_goal subst_context3: "[| p:a=b;  q:c=d;  r:e=f |]  ==>  ?p:t(a,c,e)=t(b,d,f)"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   480
  apply (erule ssubst)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   481
  apply (rule refl)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   482
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   483
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   484
(*Useful with eresolve_tac for proving equalties from known equalities.
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   485
        a = b
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   486
        |   |
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   487
        c = d   *)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   488
schematic_goal box_equals: "[| p:a=b;  q:a=c;  r:b=d |] ==> ?p:c=d"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   489
  apply (rule trans)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   490
   apply (rule trans)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   491
    apply (rule sym)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   492
    apply assumption+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   493
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   494
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   495
(*Dual of box_equals: for proving equalities backwards*)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   496
schematic_goal simp_equals: "[| p:a=c;  q:b=d;  r:c=d |] ==> ?p:a=b"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   497
  apply (rule trans)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   498
   apply (rule trans)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   499
    apply (assumption | rule sym)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   500
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   501
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   502
(** Congruence rules for predicate letters **)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   503
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   504
schematic_goal pred1_cong: "p:a=a' ==> ?p:P(a) <-> P(a')"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   505
  apply (rule iffI)
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   506
   apply (tactic \<open>
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   507
     DEPTH_SOLVE (assume_tac @{context} 1 ORELSE eresolve_tac @{context} [@{thm subst}, @{thm ssubst}] 1)\<close>)
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   508
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   509
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   510
schematic_goal pred2_cong: "[| p:a=a';  q:b=b' |] ==> ?p:P(a,b) <-> P(a',b')"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   511
  apply (rule iffI)
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   512
   apply (tactic \<open>
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   513
     DEPTH_SOLVE (assume_tac @{context} 1 ORELSE eresolve_tac @{context} [@{thm subst}, @{thm ssubst}] 1)\<close>)
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   514
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   515
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   516
schematic_goal pred3_cong: "[| p:a=a';  q:b=b';  r:c=c' |] ==> ?p:P(a,b,c) <-> P(a',b',c')"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   517
  apply (rule iffI)
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   518
   apply (tactic \<open>
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   519
     DEPTH_SOLVE (assume_tac @{context} 1 ORELSE eresolve_tac @{context} [@{thm subst}, @{thm ssubst}] 1)\<close>)
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   520
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   521
27152
192954a9a549 changed pred_congs: merely cover pred1_cong pred2_cong pred3_cong;
wenzelm
parents: 27150
diff changeset
   522
lemmas pred_congs = pred1_cong pred2_cong pred3_cong
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   523
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   524
(*special case for the equality predicate!*)
45602
2a858377c3d2 eliminated obsolete "standard";
wenzelm
parents: 45594
diff changeset
   525
lemmas eq_cong = pred2_cong [where P = "op ="]
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   526
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   527
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   528
(*** Simplifications of assumed implications.
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   529
     Roy Dyckhoff has proved that conj_impE, disj_impE, and imp_impE
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   530
     used with mp_tac (restricted to atomic formulae) is COMPLETE for
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   531
     intuitionistic propositional logic.  See
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   532
   R. Dyckhoff, Contraction-free sequent calculi for intuitionistic logic
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   533
    (preprint, University of St Andrews, 1991)  ***)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   534
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   535
schematic_goal conj_impE:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   536
  assumes major: "p:(P&Q)-->S"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   537
    and minor: "!!x. x:P-->(Q-->S) ==> q(x):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   538
  shows "?p:R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   539
  apply (assumption | rule conjI impI major [THEN mp] minor)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   540
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   541
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   542
schematic_goal disj_impE:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   543
  assumes major: "p:(P|Q)-->S"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   544
    and minor: "!!x y.[| x:P-->S; y:Q-->S |] ==> q(x,y):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   545
  shows "?p:R"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   546
  apply (tactic \<open>DEPTH_SOLVE (assume_tac @{context} 1 ORELSE
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 58963
diff changeset
   547
      resolve_tac @{context} [@{thm disjI1}, @{thm disjI2}, @{thm impI},
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   548
        @{thm major} RS @{thm mp}, @{thm minor}] 1)\<close>)
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   549
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   550
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   551
(*Simplifies the implication.  Classical version is stronger.
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   552
  Still UNSAFE since Q must be provable -- backtracking needed.  *)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   553
schematic_goal imp_impE:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   554
  assumes major: "p:(P-->Q)-->S"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   555
    and r1: "!!x y.[| x:P; y:Q-->S |] ==> q(x,y):Q"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   556
    and r2: "!!x. x:S ==> r(x):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   557
  shows "?p:R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   558
  apply (assumption | rule impI major [THEN mp] r1 r2)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   559
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   560
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   561
(*Simplifies the implication.  Classical version is stronger.
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   562
  Still UNSAFE since ~P must be provable -- backtracking needed.  *)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   563
schematic_goal not_impE:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   564
  assumes major: "p:~P --> S"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   565
    and r1: "!!y. y:P ==> q(y):False"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   566
    and r2: "!!y. y:S ==> r(y):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   567
  shows "?p:R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   568
  apply (assumption | rule notI impI major [THEN mp] r1 r2)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   569
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   570
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   571
(*Simplifies the implication.   UNSAFE.  *)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   572
schematic_goal iff_impE:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   573
  assumes major: "p:(P<->Q)-->S"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   574
    and r1: "!!x y.[| x:P; y:Q-->S |] ==> q(x,y):Q"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   575
    and r2: "!!x y.[| x:Q; y:P-->S |] ==> r(x,y):P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   576
    and r3: "!!x. x:S ==> s(x):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   577
  shows "?p:R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   578
  apply (assumption | rule iffI impI major [THEN mp] r1 r2 r3)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   579
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   580
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   581
(*What if (ALL x.~~P(x)) --> ~~(ALL x.P(x)) is an assumption? UNSAFE*)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   582
schematic_goal all_impE:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   583
  assumes major: "p:(ALL x. P(x))-->S"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   584
    and r1: "!!x. q:P(x)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   585
    and r2: "!!y. y:S ==> r(y):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   586
  shows "?p:R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   587
  apply (assumption | rule allI impI major [THEN mp] r1 r2)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   588
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   589
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   590
(*Unsafe: (EX x.P(x))-->S  is equivalent to  ALL x.P(x)-->S.  *)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   591
schematic_goal ex_impE:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   592
  assumes major: "p:(EX x. P(x))-->S"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   593
    and r: "!!y. y:P(a)-->S ==> q(y):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   594
  shows "?p:R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   595
  apply (assumption | rule exI impI major [THEN mp] r)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   596
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   597
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   598
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   599
schematic_goal rev_cut_eq:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   600
  assumes "p:a=b"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   601
    and "!!x. x:a=b ==> f(x):R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   602
  shows "?p:R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   603
  apply (rule assms)+
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   604
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   605
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   606
lemma thin_refl: "!!X. [|p:x=x; PROP W|] ==> PROP W" .
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   607
48891
c0eafbd55de3 prefer ML_file over old uses;
wenzelm
parents: 45602
diff changeset
   608
ML_file "hypsubst.ML"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   609
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   610
ML \<open>
42799
4e33894aec6d modernized functor names;
wenzelm
parents: 42616
diff changeset
   611
structure Hypsubst = Hypsubst
4e33894aec6d modernized functor names;
wenzelm
parents: 42616
diff changeset
   612
(
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   613
  (*Take apart an equality judgement; otherwise raise Match!*)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   614
  fun dest_eq (Const (@{const_name Proof}, _) $
41310
65631ca437c9 proper identifiers for consts and types;
wenzelm
parents: 39557
diff changeset
   615
    (Const (@{const_name eq}, _)  $ t $ u) $ _) = (t, u);
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   616
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   617
  val imp_intr = @{thm impI}
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   618
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   619
  (*etac rev_cut_eq moves an equality to be the last premise. *)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   620
  val rev_cut_eq = @{thm rev_cut_eq}
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   621
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   622
  val rev_mp = @{thm rev_mp}
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   623
  val subst = @{thm subst}
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   624
  val sym = @{thm sym}
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   625
  val thin_refl = @{thm thin_refl}
42799
4e33894aec6d modernized functor names;
wenzelm
parents: 42616
diff changeset
   626
);
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   627
open Hypsubst;
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   628
\<close>
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   629
48891
c0eafbd55de3 prefer ML_file over old uses;
wenzelm
parents: 45602
diff changeset
   630
ML_file "intprover.ML"
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   631
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   632
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   633
(*** Rewrite rules ***)
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   634
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   635
schematic_goal conj_rews:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   636
  "?p1 : P & True <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   637
  "?p2 : True & P <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   638
  "?p3 : P & False <-> False"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   639
  "?p4 : False & P <-> False"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   640
  "?p5 : P & P <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   641
  "?p6 : P & ~P <-> False"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   642
  "?p7 : ~P & P <-> False"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   643
  "?p8 : (P & Q) & R <-> P & (Q & R)"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   644
  apply (tactic \<open>fn st => IntPr.fast_tac @{context} 1 st\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   645
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   646
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   647
schematic_goal disj_rews:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   648
  "?p1 : P | True <-> True"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   649
  "?p2 : True | P <-> True"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   650
  "?p3 : P | False <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   651
  "?p4 : False | P <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   652
  "?p5 : P | P <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   653
  "?p6 : (P | Q) | R <-> P | (Q | R)"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   654
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   655
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   656
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   657
schematic_goal not_rews:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   658
  "?p1 : ~ False <-> True"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   659
  "?p2 : ~ True <-> False"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   660
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   661
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   662
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   663
schematic_goal imp_rews:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   664
  "?p1 : (P --> False) <-> ~P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   665
  "?p2 : (P --> True) <-> True"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   666
  "?p3 : (False --> P) <-> True"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   667
  "?p4 : (True --> P) <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   668
  "?p5 : (P --> P) <-> True"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   669
  "?p6 : (P --> ~P) <-> ~P"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   670
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   671
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   672
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   673
schematic_goal iff_rews:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   674
  "?p1 : (True <-> P) <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   675
  "?p2 : (P <-> True) <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   676
  "?p3 : (P <-> P) <-> True"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   677
  "?p4 : (False <-> P) <-> ~P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   678
  "?p5 : (P <-> False) <-> ~P"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   679
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   680
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   681
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   682
schematic_goal quant_rews:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   683
  "?p1 : (ALL x. P) <-> P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   684
  "?p2 : (EX x. P) <-> P"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   685
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   686
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   687
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   688
(*These are NOT supplied by default!*)
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   689
schematic_goal distrib_rews1:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   690
  "?p1 : ~(P|Q) <-> ~P & ~Q"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   691
  "?p2 : P & (Q | R) <-> P&Q | P&R"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   692
  "?p3 : (Q | R) & P <-> Q&P | R&P"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   693
  "?p4 : (P | Q --> R) <-> (P --> R) & (Q --> R)"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   694
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   695
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   696
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   697
schematic_goal distrib_rews2:
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   698
  "?p1 : ~(EX x. NORM(P(x))) <-> (ALL x. ~NORM(P(x)))"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   699
  "?p2 : ((EX x. NORM(P(x))) --> Q) <-> (ALL x. NORM(P(x)) --> Q)"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   700
  "?p3 : (EX x. NORM(P(x))) & NORM(Q) <-> (EX x. NORM(P(x)) & NORM(Q))"
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   701
  "?p4 : NORM(Q) & (EX x. NORM(P(x))) <-> (EX x. NORM(Q) & NORM(P(x)))"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   702
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)+
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   703
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   704
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   705
lemmas distrib_rews = distrib_rews1 distrib_rews2
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   706
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   707
schematic_goal P_Imp_P_iff_T: "p:P ==> ?p:(P <-> True)"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   708
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   709
  done
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   710
61337
4645502c3c64 fewer aliases for toplevel theorem statements;
wenzelm
parents: 60770
diff changeset
   711
schematic_goal not_P_imp_P_iff_F: "p:~P ==> ?p:(P <-> False)"
60770
240563fbf41d isabelle update_cartouches;
wenzelm
parents: 60754
diff changeset
   712
  apply (tactic \<open>IntPr.fast_tac @{context} 1\<close>)
26322
eaf634e975fa converted legacy ML scripts;
wenzelm
parents: 17480
diff changeset
   713
  done
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   714
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   715
end