diff options
| -rw-r--r-- | theories/Init/Datatypes.v | 1 | ||||
| -rw-r--r-- | theories/Init/Logic.v | 19 |
2 files changed, 19 insertions, 1 deletions
diff --git a/theories/Init/Datatypes.v b/theories/Init/Datatypes.v index ddaf08bf71..4e3f2e80f3 100644 --- a/theories/Init/Datatypes.v +++ b/theories/Init/Datatypes.v @@ -326,7 +326,6 @@ Lemma CompSpec2Type : forall A (eq lt:A->A->Prop) x y c, CompSpec eq lt x y c -> CompSpecT eq lt x y c. Proof. intros. apply CompareSpec2Type; assumption. Defined. - (******************************************************************) (** * Misc Other Datatypes *) diff --git a/theories/Init/Logic.v b/theories/Init/Logic.v index 85123cc444..fb1a7ab1c1 100644 --- a/theories/Init/Logic.v +++ b/theories/Init/Logic.v @@ -125,6 +125,25 @@ Proof. [apply Hl | apply Hr]; assumption. Qed. +Theorem imp_iff_compat_l : forall A B C : Prop, + (B <-> C) -> ((A -> B) <-> (A -> C)). +Proof. + intros ? ? ? [Hl Hr]; split; intros H ?; [apply Hl | apply Hr]; apply H; assumption. +Qed. + +Theorem imp_iff_compat_r : forall A B C : Prop, + (B <-> C) -> ((B -> A) <-> (C -> A)). +Proof. + intros ? ? ? [Hl Hr]; split; intros H ?; [apply H, Hr | apply H, Hl]; assumption. +Qed. + +Theorem not_iff_compat : forall A B : Prop, + (A <-> B) -> (~ A <-> ~B). +Proof. + intros; apply imp_iff_compat_r; assumption. +Qed. + + (** Some equivalences *) Theorem neg_false : forall A : Prop, ~ A <-> (A <-> False). |