src/HOL/simpdata.ML
 changeset 4743 b3bfcbd9fb93 parent 4718 fc2ba9fb2135 child 4744 4469d498cd48
equal inserted replaced
4742:a25bb8a260ae 4743:b3bfcbd9fb93
`   206 `
`   206 `
`   207 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";`
`   207 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";`
`   208 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";`
`   208 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";`
`   209 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";`
`   209 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";`
`   210 prove "not_iff" "(P~=Q) = (P = (~Q))";`
`   210 prove "not_iff" "(P~=Q) = (P = (~Q))";`
`   211 prove "not1_or" "(~P | Q) = (P --> Q)";`
`   211 prove "disj_not1" "(~P | Q) = (P --> Q)";`
`   212 prove "not2_or" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)`
`   212 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)`
`   213 `
`   213 `
`   214 (*Avoids duplication of subgoals after expand_if, when the true and false `
`   214 (*Avoids duplication of subgoals after expand_if, when the true and false `
`   215   cases boil down to the same thing.*) `
`   215   cases boil down to the same thing.*) `
`   216 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";`
`   216 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";`
`   217 `
`   217 `
`   408      ([triv_forall_equality, (* prunes params *)`
`   408      ([triv_forall_equality, (* prunes params *)`
`   409        True_implies_equals, (* prune asms `True' *)`
`   409        True_implies_equals, (* prune asms `True' *)`
`   410        if_True, if_False, if_cancel, if_eq_cancel,`
`   410        if_True, if_False, if_cancel, if_eq_cancel,`
`   411        o_apply, imp_disjL, conj_assoc, disj_assoc,`
`   411        o_apply, imp_disjL, conj_assoc, disj_assoc,`
`   412        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,`
`   412        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,`
`   413        not1_or, not_all, not_ex, cases_simp]`
`   413        disj_not1, not_all, not_ex, cases_simp]`
`   414      @ ex_simps @ all_simps @ simp_thms)`
`   414      @ ex_simps @ all_simps @ simp_thms)`
`   415      addsimprocs [defALL_regroup,defEX_regroup]`
`   415      addsimprocs [defALL_regroup,defEX_regroup]`
`   416      addcongs [imp_cong];`
`   416      addcongs [imp_cong];`
`   417 `
`   417 `
`   418 qed_goal "if_distrib" HOL.thy`
`   418 qed_goal "if_distrib" HOL.thy`