diff options
Diffstat (limited to 'theories/Vectors/VectorSpec.v')
| -rw-r--r-- | theories/Vectors/VectorSpec.v | 39 |
1 files changed, 35 insertions, 4 deletions
diff --git a/theories/Vectors/VectorSpec.v b/theories/Vectors/VectorSpec.v index c5278b91..34dbaf36 100644 --- a/theories/Vectors/VectorSpec.v +++ b/theories/Vectors/VectorSpec.v @@ -1,9 +1,11 @@ (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) (* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) (************************************************************************) (** Proofs of specification for functions defined over Vector @@ -122,3 +124,32 @@ induction l. - reflexivity. - unfold to_list; simpl. now f_equal. Qed. + +Lemma take_O : forall {A} {n} le (v:t A n), take 0 le v = []. +Proof. + reflexivity. +Qed. + +Lemma take_idem : forall {A} p n (v:t A n) le le', + take p le' (take p le v) = take p le v. +Proof. + induction p; intros n v le le'. + - auto. + - destruct v. inversion le. simpl. apply f_equal. apply IHp. +Qed. + +Lemma take_app : forall {A} {n} (v:t A n) {m} (w:t A m) le, take n le (append v w) = v. +Proof. + induction v; intros m w le. + - reflexivity. + - simpl. apply f_equal. apply IHv. +Qed. + +(* Proof is irrelevant for [take] *) +Lemma take_prf_irr : forall {A} p {n} (v:t A n) le le', take p le v = take p le' v. +Proof. + induction p; intros n v le le'. + - reflexivity. + - destruct v. inversion le. simpl. apply f_equal. apply IHp. +Qed. + |