(* Title: FOL/FOL.thy
ID: $Id$
Author: Lawrence C Paulson and Markus Wenzel
Classical first-order logic.
This may serve as a good example of initializing all the tools and
packages required for a reasonable working environment. Please go
elsewhere to see actual applications!
*)
theory FOL = IFOL
files
("FOL_lemmas1.ML") ("cladata.ML") ("blastdata.ML")
("simpdata.ML") ("FOL_lemmas2.ML"):
subsection {* The classical axiom *}
axioms
classical: "(~P ==> P) ==> P"
subsection {* Setup of several proof tools *}
use "FOL_lemmas1.ML"
use "cladata.ML"
setup Cla.setup
setup clasetup
lemma all_eq: "(!!x. P(x)) == Trueprop (ALL x. P(x))"
proof (rule equal_intr_rule)
assume "!!x. P(x)"
show "ALL x. P(x)" ..
next
assume "ALL x. P(x)"
thus "!!x. P(x)" ..
qed
lemma imp_eq: "(A ==> B) == Trueprop (A --> B)"
proof (rule equal_intr_rule)
assume r: "A ==> B"
show "A --> B"
by (rule) (rule r)
next
assume "A --> B" and A
thus B ..
qed
lemmas atomize = all_eq imp_eq
use "blastdata.ML"
setup Blast.setup
use "FOL_lemmas2.ML"
use "simpdata.ML"
setup simpsetup
setup cong_attrib_setup
setup "Simplifier.method_setup Splitter.split_modifiers"
setup Splitter.setup
setup Clasimp.setup
subsection {* Calculational rules *}
lemma forw_subst: "a = b ==> P(b) ==> P(a)"
by (rule ssubst)
lemma back_subst: "P(a) ==> a = b ==> P(b)"
by (rule subst)
text {*
Note that this list of rules is in reverse order of priorities.
*}
lemmas trans_rules [trans] =
forw_subst
back_subst
rev_mp
mp
trans
lemmas [elim?] = sym
end