diff options
author | pboutill <pboutill@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-02-10 14:11:14 +0000 |
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committer | pboutill <pboutill@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-02-10 14:11:14 +0000 |
commit | 461a5a2093f8e46708e01a27993f80919e20d4aa (patch) | |
tree | 1e66ec78daccfa700b9461dadefb34800ac598b9 /theories/Vectors/VectorSpec.v | |
parent | 27ab4eb203dd5d653724f7a1af61badf2916c349 (diff) |
Vectors fully use implicit arguments
and take disavantages for maximal insertion
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13827 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Vectors/VectorSpec.v')
-rw-r--r-- | theories/Vectors/VectorSpec.v | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/theories/Vectors/VectorSpec.v b/theories/Vectors/VectorSpec.v index 1fa70a60c..a576315e6 100644 --- a/theories/Vectors/VectorSpec.v +++ b/theories/Vectors/VectorSpec.v @@ -23,7 +23,7 @@ Lemma eq_nth_iff A n (v1 v2: t A n): (forall p1 p2, p1 = p2 -> v1 [@ p1 ] = v2 [@ p2 ]) <-> v1 = v2. Proof. split. - revert n v1 v2; refine (rect2 _ _ _); simpl; intros. + revert n v1 v2; refine (@rect2 _ _ _ _ _); simpl; intros. reflexivity. f_equal. apply (H0 Fin.F1 Fin.F1 eq_refl). apply H. intros p1 p2 H1; @@ -34,7 +34,7 @@ Qed. Lemma nth_order_last A: forall n (v: t A (S n)) (H: n < S n), nth_order v H = last v. Proof. -unfold nth_order; refine (rectS _ _ _); now simpl. +unfold nth_order; refine (@rectS _ _ _ _); now simpl. Qed. Lemma shiftin_nth A a n (v: t A n) k1 k2 (eq: k1 = k2): @@ -42,7 +42,7 @@ Lemma shiftin_nth A a n (v: t A n) k1 k2 (eq: k1 = k2): Proof. subst k2; induction k1. generalize dependent n. apply caseS ; intros. now simpl. - generalize dependent n. refine (caseS _ _) ; intros. now simpl. + generalize dependent n. refine (@caseS _ _ _) ; intros. now simpl. Qed. Lemma shiftin_last A a n (v: t A n): last (shiftin a v) = a. @@ -53,8 +53,8 @@ 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. - revert n v; refine (caseS _ _); simpl; intros. now destruct t. +refine (@Fin.rectS _ _ _); intros. + 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 |S (S n) => fun v => forall p : Fin.t (S n), @@ -66,7 +66,7 @@ Qed. Lemma shiftrepeat_last A: forall n (v: t A (S n)), last (shiftrepeat v) = last v. Proof. -refine (rectS _ _ _); now simpl. +refine (@rectS _ _ _ _); now simpl. Qed. Lemma const_nth A (a: A) n (p: Fin.t n): (const a n)[@ p] = a. @@ -78,17 +78,17 @@ Lemma nth_map {A B} (f: A -> B) {n} v (p1 p2: Fin.t n) (eq: p1 = p2): (map f v) [@ p1] = f (v [@ p2]). Proof. subst p2; induction p1. - revert n v; refine (caseS _ _); now simpl. - revert n v p1 IHp1; refine (caseS _ _); now simpl. + revert n v; refine (@caseS _ _ _); now simpl. + revert n v p1 IHp1; refine (@caseS _ _ _); now simpl. Qed. Lemma nth_map2 {A B C} (f: A -> B -> C) {n} v w (p1 p2 p3: Fin.t n): p1 = p2 -> p2 = p3 -> (map2 f v w) [@p1] = f (v[@p2]) (w[@p3]). Proof. intros; subst p2; subst p3; revert n v w p1. -refine (rect2 _ _ _); simpl. - exact (Fin.case0). - intros n v1 v2 H a b p; revert n p v1 v2 H; refine (Fin.caseS _ _ _); +refine (@rect2 _ _ _ _ _); simpl. + exact (Fin.case0 _). + intros n v1 v2 H a b p; revert n p v1 v2 H; refine (@Fin.caseS _ _ _); now simpl. Qed. |