# Theory Metis

```(*  Title:      HOL/Metis.thy
Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory
Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
Author:     Jasmin Blanchette, TU Muenchen
*)

section ‹Metis Proof Method›

theory Metis
imports ATP
begin

ML_file ‹~~/src/Tools/Metis/metis.ML›

subsection ‹Literal selection and lambda-lifting helpers›

definition select :: "'a ⇒ 'a" where
"select = (λx. x)"

lemma not_atomize: "(¬ A ⟹ False) ≡ Trueprop A"
by (cut_tac atomize_not [of "¬ A"]) simp

lemma atomize_not_select: "(A ⟹ select False) ≡ Trueprop (¬ A)"
unfolding select_def by (rule atomize_not)

lemma not_atomize_select: "(¬ A ⟹ select False) ≡ Trueprop A"
unfolding select_def by (rule not_atomize)

lemma select_FalseI: "False ⟹ select False"
by simp

definition lambda :: "'a ⇒ 'a" where
"lambda = (λx. x)"

lemma eq_lambdaI: "x ≡ y ⟹ x ≡ lambda y"
unfolding lambda_def by assumption

subsection ‹Metis package›

ML_file ‹Tools/Metis/metis_generate.ML›
ML_file ‹Tools/Metis/metis_reconstruct.ML›
ML_file ‹Tools/Metis/metis_tactic.ML›

hide_const (open) select fFalse fTrue fNot fComp fconj fdisj fimplies fAll fEx fequal lambda
hide_fact (open) select_def not_atomize atomize_not_select not_atomize_select select_FalseI
fFalse_def fTrue_def fNot_def fconj_def fdisj_def fimplies_def fAll_def fEx_def fequal_def
fTrue_ne_fFalse fNot_table fconj_table fdisj_table fimplies_table fAll_table fEx_table
fequal_table fAll_table fEx_table fNot_law fComp_law fconj_laws fdisj_laws fimplies_laws
fequal_laws fAll_law fEx_law lambda_def eq_lambdaI

end
```