diff options
Diffstat (limited to 'theories/Logic/Classical_Prop.v')
| -rw-r--r-- | theories/Logic/Classical_Prop.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Logic/Classical_Prop.v b/theories/Logic/Classical_Prop.v index 8d2e946de..df732959f 100644 --- a/theories/Logic/Classical_Prop.v +++ b/theories/Logic/Classical_Prop.v @@ -22,7 +22,7 @@ unfold not in |- *; intros; elim (classic p); auto. intro NP; elim (H NP). Qed. -(** Peirce's law states [forall P Q:Prop, ((P -> Q) -> P) -> P]. +(** Peirce's law states [forall P Q:Prop, ((P -> Q) -> P) -> P]. Thanks to [forall P, False -> P], it is equivalent to the following form *) @@ -95,11 +95,11 @@ Proof proof_irrelevance_cci classic. (* classical_left transforms |- A \/ B into ~B |- A *) (* classical_right transforms |- A \/ B into ~A |- B *) -Ltac classical_right := match goal with +Ltac classical_right := match goal with | _:_ |-?X1 \/ _ => (elim (classic X1);intro;[left;trivial|right]) end. -Ltac classical_left := match goal with +Ltac classical_left := match goal with | _:_ |- _ \/?X1 => (elim (classic X1);intro;[right;trivial|left]) end. @@ -107,7 +107,7 @@ Require Export EqdepFacts. Module Eq_rect_eq. -Lemma eq_rect_eq : +Lemma eq_rect_eq : forall (U:Type) (p:U) (Q:U -> Type) (x:Q p) (h:p = p), x = eq_rect p Q x p h. Proof. intros; rewrite proof_irrelevance with (p1:=h) (p2:=refl_equal p); reflexivity. |