diff options
Diffstat (limited to 'theories/Logic')
-rwxr-xr-x | theories/Logic/Classical_Pred_Set.v | 45 | ||||
-rwxr-xr-x | theories/Logic/Classical_Type.v | 4 |
2 files changed, 14 insertions, 35 deletions
diff --git a/theories/Logic/Classical_Pred_Set.v b/theories/Logic/Classical_Pred_Set.v index 8a88642f3..0b0c329be 100755 --- a/theories/Logic/Classical_Pred_Set.v +++ b/theories/Logic/Classical_Pred_Set.v @@ -8,9 +8,12 @@ (*i $Id$ i*) +(** This file is obsolete, use Classical_Pred_Type.v via Classical.v +instead *) + (** Classical Predicate Logic on Set*) -Require Import Classical_Prop. +Require Import Classical_Pred_Type. Section Generic. Variable U : Set. @@ -19,52 +22,26 @@ Variable U : Set. Lemma not_all_ex_not : forall P:U -> Prop, ~ (forall n:U, P n) -> exists n : U, ~ P n. -Proof. -unfold not in |- *; intros P notall. -apply NNPP; unfold not in |- *. -intro abs. -cut (forall n:U, P n); auto. -intro n; apply NNPP. -unfold not in |- *; intros. -apply abs; exists n; trivial. -Qed. +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. -intros P H. -elim (not_all_ex_not (fun n:U => ~ P n) H); intros n Pn; exists n. -apply NNPP; trivial. -Qed. +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. -unfold not in |- *; intros P notex n abs. -apply notex. -exists n; trivial. -Qed. +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. -intros P H n. -apply NNPP. -red in |- *; intro K; apply H; exists n; trivial. -Qed. +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. -unfold not in |- *; intros P exnot allP. -elim exnot; auto. -Qed. +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. -unfold not in |- *; intros P allnot exP; elim exP; intros n p. -apply allnot with n; auto. -Qed. +Proof (Classical_Pred_Type.all_not_not_ex U). -End Generic.
\ No newline at end of file +End Generic. diff --git a/theories/Logic/Classical_Type.v b/theories/Logic/Classical_Type.v index fc5d162a2..3b91afd02 100755 --- a/theories/Logic/Classical_Type.v +++ b/theories/Logic/Classical_Type.v @@ -8,7 +8,9 @@ (*i $Id$ i*) +(** This file is obsolete, use Classical.v instead *) + (** Classical Logic for Type *) Require Export Classical_Prop. -Require Export Classical_Pred_Type.
\ No newline at end of file +Require Export Classical_Pred_Type. |