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Diffstat (limited to 'theories/Logic/Classical_Pred_Set.v')
-rw-r--r-- | theories/Logic/Classical_Pred_Set.v | 48 |
1 files changed, 0 insertions, 48 deletions
diff --git a/theories/Logic/Classical_Pred_Set.v b/theories/Logic/Classical_Pred_Set.v deleted file mode 100644 index d634217f..00000000 --- a/theories/Logic/Classical_Pred_Set.v +++ /dev/null @@ -1,48 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) - -(* File created for Coq V5.10.14b, Oct 1995, by duplication of - Classical_Pred_Type.v *) - -(** This file is obsolete, use Classical_Pred_Type.v via Classical.v -instead *) - -(** Classical Predicate Logic on Set*) - -Require Import Classical_Pred_Type. - -Section Generic. -Variable U : Set. - -(** de Morgan laws for quantifiers *) - -Lemma not_all_ex_not : - forall P:U -> Prop, ~ (forall n:U, P n) -> exists n : U, ~ P n. -Proof (Classical_Pred_Type.not_all_ex_not U). - -Lemma not_all_not_ex : - forall P:U -> Prop, ~ (forall n:U, ~ P n) -> exists n : U, P n. -Proof (Classical_Pred_Type.not_all_not_ex U). - -Lemma not_ex_all_not : - forall P:U -> Prop, ~ (exists n : U, P n) -> forall n:U, ~ P n. -Proof (Classical_Pred_Type.not_ex_all_not U). - -Lemma not_ex_not_all : - forall P:U -> Prop, ~ (exists n : U, ~ P n) -> forall n:U, P n. -Proof (Classical_Pred_Type.not_ex_not_all U). - -Lemma ex_not_not_all : - forall P:U -> Prop, (exists n : U, ~ P n) -> ~ (forall n:U, P n). -Proof (Classical_Pred_Type.ex_not_not_all U). - -Lemma all_not_not_ex : - forall P:U -> Prop, (forall n:U, ~ P n) -> ~ (exists n : U, P n). -Proof (Classical_Pred_Type.all_not_not_ex U). - -End Generic. |