diff options
Diffstat (limited to 'theories/Vectors/VectorSpec.v')
| -rw-r--r-- | theories/Vectors/VectorSpec.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Vectors/VectorSpec.v b/theories/Vectors/VectorSpec.v index 2f4086e5..7f4228dd 100644 --- a/theories/Vectors/VectorSpec.v +++ b/theories/Vectors/VectorSpec.v @@ -16,7 +16,7 @@ Require Fin. Require Import VectorDef. Import VectorNotations. -Definition cons_inj A a1 a2 n (v1 v2 : t A n) +Definition cons_inj {A} {a1 a2} {n} {v1 v2 : t A n} (eq : a1 :: v1 = a2 :: v2) : a1 = a2 /\ v1 = v2 := match eq in _ = x return caseS _ (fun a2' _ v2' => fun v1' => a1 = a2' /\ v1' = v2') x v1 with | eq_refl => conj eq_refl eq_refl @@ -59,15 +59,15 @@ Qed. Lemma shiftrepeat_nth A: forall n k (v: t A (S n)), nth (shiftrepeat v) (Fin.L_R 1 k) = nth v k. Proof. -refine (@Fin.rectS _ _ _); intros. +refine (@Fin.rectS _ _ _); lazy beta; [ intros n v | intros n p H v ]. revert n v; refine (@caseS _ _ _); simpl; intros. now destruct t. revert p H. - refine (match v as v' in t _ m return match m as m' return t A m' -> Type with + refine (match v as v' in t _ m return match m as m' return t A m' -> Prop with |S (S n) => fun v => forall p : Fin.t (S n), (forall v0 : t A (S n), (shiftrepeat v0) [@ Fin.L_R 1 p ] = v0 [@p]) -> (shiftrepeat v) [@Fin.L_R 1 (Fin.FS p)] = v [@Fin.FS p] - |_ => fun _ => @ID end v' with - |[] => @id |h :: t => _ end). destruct n0. exact @id. now simpl. + |_ => fun _ => True end v' with + |[] => I |h :: t => _ end). destruct n0. exact I. now simpl. Qed. Lemma shiftrepeat_last A: forall n (v: t A (S n)), last (shiftrepeat v) = last v. @@ -105,7 +105,7 @@ Proof. assert (forall n h (v: t B n) a, fold_left f (f a h) v = f (fold_left f a v) h). induction v0. now simpl. - intros; simpl. rewrite<- IHv0. now f_equal. + intros; simpl. rewrite<- IHv0, assoc. now f_equal. induction v. reflexivity. simpl. intros; now rewrite<- (IHv). |