diff options
| author |  Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2015-12-07 10:52:14 +0100 |
|---|---|---|
| committer | Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2015-12-07 10:52:24 +0100 |
| commit | df3a49a18c5b01984000df9244ecea9c275b30cd (patch) | |
| tree | d14afdb5de5f93e4301f8eba8bddecd5a6597f9a /theories/Numbers | |
| parent | fe2776f9e0d355cccb0841495a9843351d340066 (diff) | |
Fix some typos.
Diffstat (limited to 'theories/Numbers')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivEucl.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivFloor.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivTrunc.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/NatInt/NZDiv.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Natural/Abstract/NDiv.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Natural/Abstract/NParity.v | 2 |
6 files changed, 6 insertions, 6 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZDivEucl.v b/theories/Numbers/Integer/Abstract/ZDivEucl.v index d0df8fb4a..ab73ebfe1 100644 --- a/theories/Numbers/Integer/Abstract/ZDivEucl.v +++ b/theories/Numbers/Integer/Abstract/ZDivEucl.v @@ -391,7 +391,7 @@ rewrite <- (add_0_r (b*(a/b))) at 2. apply add_cancel_l. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, 0<b -> a < b*q -> a/b < q. diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v index d5f3f4ada..c8260e516 100644 --- a/theories/Numbers/Integer/Abstract/ZDivFloor.v +++ b/theories/Numbers/Integer/Abstract/ZDivFloor.v @@ -436,7 +436,7 @@ rewrite <- (add_0_r (b*(a/b))) at 2. apply add_cancel_l. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, 0<b -> a < b*q -> a/b < q. diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v index de2e99ec3..464fe354b 100644 --- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v +++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.v @@ -404,7 +404,7 @@ Proof. intros. rewrite rem_eq by order. rewrite sub_move_r; nzsimpl; tauto. Qed. -(** Some additionnal inequalities about quot. *) +(** Some additional inequalities about quot. *) Theorem quot_lt_upper_bound: forall a b q, 0<=a -> 0<b -> a < b*q -> a÷b < q. diff --git a/theories/Numbers/NatInt/NZDiv.v b/theories/Numbers/NatInt/NZDiv.v index 4a127216f..e0dfdedbd 100644 --- a/theories/Numbers/NatInt/NZDiv.v +++ b/theories/Numbers/NatInt/NZDiv.v @@ -307,7 +307,7 @@ rewrite <- (add_0_r (b*(a/b))) at 2. apply add_cancel_l. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, 0<=a -> 0<b -> a < b*q -> a/b < q. diff --git a/theories/Numbers/Natural/Abstract/NDiv.v b/theories/Numbers/Natural/Abstract/NDiv.v index fb68c139b..d3d3eb0fb 100644 --- a/theories/Numbers/Natural/Abstract/NDiv.v +++ b/theories/Numbers/Natural/Abstract/NDiv.v @@ -137,7 +137,7 @@ Proof. intros; apply mul_succ_div_gt; auto'. Qed. Lemma div_exact : forall a b, b~=0 -> (a == b*(a/b) <-> a mod b == 0). Proof. intros. apply div_exact; auto'. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, b~=0 -> a < b*q -> a/b < q. diff --git a/theories/Numbers/Natural/Abstract/NParity.v b/theories/Numbers/Natural/Abstract/NParity.v index b3526c9a1..80a579f19 100644 --- a/theories/Numbers/Natural/Abstract/NParity.v +++ b/theories/Numbers/Natural/Abstract/NParity.v @@ -8,7 +8,7 @@ Require Import Bool NSub NZParity. -(** Some additionnal properties of [even], [odd]. *) +(** Some additional properties of [even], [odd]. *) Module Type NParityProp (Import N : NAxiomsSig')(Import NP : NSubProp N). |