src/FOL/FOL.thy
 author wenzelm Wed, 31 Oct 2001 01:19:58 +0100 changeset 11988 8340fb172607 parent 11848 6e3017adb8c0 child 12127 219e543496a3 permissions -rw-r--r--
induct_impliesI;

(*  Title:      FOL/FOL.thy
ID:         \$Id\$
Author:     Lawrence C Paulson and Markus Wenzel
*)

header {* Classical first-order logic *}

theory FOL = IFOL
files
("simpdata.ML") ("FOL_lemmas2.ML"):

subsection {* The classical axiom *}

axioms
classical: "(~P ==> P) ==> P"

subsection {* Lemmas and proof tools *}

use "FOL_lemmas1.ML"
theorems case_split = case_split_thm [case_names True False]

setup Cla.setup
setup clasetup

use "blastdata.ML"
setup Blast.setup
use "FOL_lemmas2.ML"

use "simpdata.ML"
setup simpsetup
setup "Simplifier.method_setup Splitter.split_modifiers"
setup Splitter.setup
setup Clasimp.setup

subsection {* Proof by cases and induction *}

text {* Proper handling of non-atomic rule statements. *}

constdefs
induct_forall :: "('a => o) => o"
"induct_forall(P) == \<forall>x. P(x)"
induct_implies :: "o => o => o"
"induct_implies(A, B) == A --> B"
induct_equal :: "'a => 'a => o"
"induct_equal(x, y) == x = y"

lemma induct_forall_eq: "(!!x. P(x)) == Trueprop(induct_forall(\<lambda>x. P(x)))"
by (simp only: atomize_all induct_forall_def)

lemma induct_implies_eq: "(A ==> B) == Trueprop(induct_implies(A, B))"
by (simp only: atomize_imp induct_implies_def)

lemma induct_equal_eq: "(x == y) == Trueprop(induct_equal(x, y))"
by (simp only: atomize_eq induct_equal_def)

lemma induct_impliesI: "(A ==> B) ==> induct_implies(A, B)"

lemmas induct_atomize = induct_forall_eq induct_implies_eq induct_equal_eq
lemmas induct_rulify1 = induct_atomize [symmetric, standard]
lemmas induct_rulify2 = induct_forall_def induct_implies_def induct_equal_def

hide const induct_forall induct_implies induct_equal

text {* Method setup. *}

ML {*
structure InductMethod = InductMethodFun
(struct
val dest_concls = FOLogic.dest_concls;
val cases_default = thm "case_split";
val local_impI = thm "induct_impliesI";
val conjI = thm "conjI";
val atomize = thms "induct_atomize";
val rulify1 = thms "induct_rulify1";
val rulify2 = thms "induct_rulify2";
end);
*}

setup InductMethod.setup

end