From df3a49a18c5b01984000df9244ecea9c275b30cd Mon Sep 17 00:00:00 2001 From: Guillaume Melquiond Date: Mon, 7 Dec 2015 10:52:14 +0100 Subject: Fix some typos. --- theories/ZArith/Zdiv.v | 2 +- theories/ZArith/Zpow_alt.v | 2 +- theories/ZArith/Zquot.v | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) (limited to 'theories/ZArith') diff --git a/theories/ZArith/Zdiv.v b/theories/ZArith/Zdiv.v index d0d10891a..363b4fd03 100644 --- a/theories/ZArith/Zdiv.v +++ b/theories/ZArith/Zdiv.v @@ -279,7 +279,7 @@ Proof. intros; rewrite Z.div_exact; auto. Qed. Theorem Zmod_le: forall a b, 0 < b -> 0 <= a -> a mod b <= a. Proof. intros. apply Z.mod_le; auto. Qed. -(** Some additionnal inequalities about Z.div. *) +(** Some additional inequalities about Z.div. *) Theorem Zdiv_lt_upper_bound: forall a b q, 0 < b -> a < q*b -> a/b < q. diff --git a/theories/ZArith/Zpow_alt.v b/theories/ZArith/Zpow_alt.v index 8f661a9c8..c8627477b 100644 --- a/theories/ZArith/Zpow_alt.v +++ b/theories/ZArith/Zpow_alt.v @@ -11,7 +11,7 @@ Local Open Scope Z_scope. (** An alternative power function for Z *) -(** This [Zpower_alt] is extensionnaly equal to [Z.pow], +(** This [Zpower_alt] is extensionally equal to [Z.pow], but not convertible with it. The number of multiplications is logarithmic instead of linear, but these multiplications are bigger. Experimentally, it seems diff --git a/theories/ZArith/Zquot.v b/theories/ZArith/Zquot.v index 3ef111898..6db92edb7 100644 --- a/theories/ZArith/Zquot.v +++ b/theories/ZArith/Zquot.v @@ -243,7 +243,7 @@ Proof. intros. zero_or_not b. intuition. apply Z.quot_exact; auto. Qed. Theorem Zrem_le a b : 0 <= a -> 0 <= b -> Z.rem a b <= a. Proof. intros. zero_or_not b. apply Z.rem_le; auto with zarith. Qed. -(** Some additionnal inequalities about Zdiv. *) +(** Some additional inequalities about Zdiv. *) Theorem Zquot_le_upper_bound: forall a b q, 0 < b -> a <= q*b -> a÷b <= q. -- cgit v1.2.3