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src/FOL/FOL.thy

author | wenzelm |

Thu, 04 Oct 2001 15:28:26 +0200 | |

changeset 11678 | 6aa3e2d26683 |

parent 11096 | bedfd42db838 |

child 11771 | b7b100a2de1d |

permissions | -rw-r--r-- |

moved atomize stuff to theory IFOL;
added induct/cases setup;

(* Title: FOL/FOL.thy ID: $Id$ Author: Lawrence C Paulson and Markus Wenzel *) header {* Classical first-order logic *} 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 {* Lemmas and proof tools *} use "FOL_lemmas1.ML" theorems case_split = case_split_thm [case_names True False] use "cladata.ML" 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 setup Rulify.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) 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 conjI = thm "conjI"; val atomize = thms "induct_atomize"; val rulify1 = thms "induct_rulify1"; val rulify2 = thms "induct_rulify2"; end); *} setup InductMethod.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 transitive trans lemmas [elim?] = sym end