diff options
Diffstat (limited to 'theories/Logic')
| -rwxr-xr-x | theories/Logic/Classical_Pred_Type.v | 29 |
1 files changed, 15 insertions, 14 deletions
diff --git a/theories/Logic/Classical_Pred_Type.v b/theories/Logic/Classical_Pred_Type.v index 1c1292fc8..ef4e89793 100755 --- a/theories/Logic/Classical_Pred_Type.v +++ b/theories/Logic/Classical_Pred_Type.v @@ -17,24 +17,25 @@ Variable U : Type. (** de Morgan laws for quantifiers *) -Lemma not_all_ex_not : - forall P:U -> Prop, ~ (forall n:U, P n) -> exists n : U, ~ P n. +Lemma not_all_not_ex : + 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 |- *. +intros P notall. +apply NNPP. intro abs. -cut (forall n:U, P n); auto. -intro n; apply NNPP. -unfold not in |- *; intros. -apply abs; exists n; trivial. +apply notall. +intros n H. +apply abs; exists n; exact H. Qed. -Lemma not_all_not_ex : - forall P:U -> Prop, ~ (forall n:U, ~ P n) -> exists n : U, P n. +Lemma not_all_ex_not : + 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. +intros P notall. +apply not_all_not_ex with (P:=fun x => ~ P x). +intro all; apply notall. +intro n; apply NNPP. +apply all. Qed. Lemma not_ex_all_not : @@ -67,4 +68,4 @@ unfold not in |- *; intros P allnot exP; elim exP; intros n p. apply allnot with n; auto. Qed. -End Generic.
\ No newline at end of file +End Generic. |