diff options
| author |  Hugo Herbelin <Hugo.Herbelin@inria.fr> | 2014-06-01 10:26:26 +0200 |
|---|---|---|
| committer | Hugo Herbelin <Hugo.Herbelin@inria.fr> | 2014-06-01 11:33:55 +0200 |
| commit | 76adb57c72fccb4f3e416bd7f3927f4fff72178b (patch) | |
| tree | f8d72073a2ea62d3e5c274c201ef06532ac57b61 /theories/Structures | |
| parent | be01deca2b8ff22505adaa66f55f005673bf2d85 (diff) | |
Making those proofs which depend on names generated for the arguments
in Prop of constructors of inductive types independent of these names.
Incidentally upgraded/simplified a couple of proofs, mainly in Reals.
This prepares to the next commit about using names based on H for such
hypotheses in Prop.
Diffstat (limited to 'theories/Structures')
| -rw-r--r-- | theories/Structures/DecidableTypeEx.v | 2 | ||||
| -rw-r--r-- | theories/Structures/EqualitiesFacts.v | 2 | ||||
| -rw-r--r-- | theories/Structures/OrderedType.v | 8 | ||||
| -rw-r--r-- | theories/Structures/OrderedTypeEx.v | 4 |
4 files changed, 8 insertions, 8 deletions
diff --git a/theories/Structures/DecidableTypeEx.v b/theories/Structures/DecidableTypeEx.v index 971fcd7f8..163a40f2e 100644 --- a/theories/Structures/DecidableTypeEx.v +++ b/theories/Structures/DecidableTypeEx.v @@ -88,7 +88,7 @@ Module PairUsualDecidableType(D1 D2:UsualDecidableType) <: UsualDecidableType. destruct (D1.eq_dec x1 y1); destruct (D2.eq_dec x2 y2); unfold eq, D1.eq, D2.eq in *; simpl; (left; f_equal; auto; fail) || - (right; intro H; injection H; auto). + (right; injection; auto). Defined. End PairUsualDecidableType. diff --git a/theories/Structures/EqualitiesFacts.v b/theories/Structures/EqualitiesFacts.v index c69885b46..11d94c119 100644 --- a/theories/Structures/EqualitiesFacts.v +++ b/theories/Structures/EqualitiesFacts.v @@ -166,7 +166,7 @@ Module PairUsualDecidableType(D1 D2:UsualDecidableType) <: UsualDecidableType. destruct (D1.eq_dec x1 y1); destruct (D2.eq_dec x2 y2); unfold eq, D1.eq, D2.eq in *; simpl; (left; f_equal; auto; fail) || - (right; intro H; injection H; auto). + (right; intros [=]; auto). Defined. End PairUsualDecidableType. diff --git a/theories/Structures/OrderedType.v b/theories/Structures/OrderedType.v index fa08f9366..b9510342c 100644 --- a/theories/Structures/OrderedType.v +++ b/theories/Structures/OrderedType.v @@ -85,16 +85,16 @@ Module OrderedTypeFacts (Import O: OrderedType). Lemma lt_eq : forall x y z, lt x y -> eq y z -> lt x z. Proof. - intros; destruct (compare x z); auto. + intros; destruct (compare x z) as [Hlt|Heq|Hlt]; auto. elim (lt_not_eq H); apply eq_trans with z; auto. - elim (lt_not_eq (lt_trans l H)); auto. + elim (lt_not_eq (lt_trans Hlt H)); auto. Qed. Lemma eq_lt : forall x y z, eq x y -> lt y z -> lt x z. Proof. - intros; destruct (compare x z); auto. + intros; destruct (compare x z) as [Hlt|Heq|Hlt]; auto. elim (lt_not_eq H0); apply eq_trans with x; auto. - elim (lt_not_eq (lt_trans H0 l)); auto. + elim (lt_not_eq (lt_trans H0 Hlt)); auto. Qed. Instance lt_compat : Proper (eq==>eq==>iff) lt. diff --git a/theories/Structures/OrderedTypeEx.v b/theories/Structures/OrderedTypeEx.v index 83130deb2..3c6afc7b2 100644 --- a/theories/Structures/OrderedTypeEx.v +++ b/theories/Structures/OrderedTypeEx.v @@ -279,7 +279,7 @@ Module PositiveOrderedTypeBits <: UsualOrderedType. Proof. induction x; destruct y. - (* I I *) - destruct (IHx y). + destruct (IHx y) as [l|e|g]. apply LT; auto. apply EQ; rewrite e; red; auto. apply GT; auto. @@ -290,7 +290,7 @@ Module PositiveOrderedTypeBits <: UsualOrderedType. - (* O I *) apply LT; simpl; auto. - (* O O *) - destruct (IHx y). + destruct (IHx y) as [l|e|g]. apply LT; auto. apply EQ; rewrite e; red; auto. apply GT; auto. |