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-rw-r--r--theories/Numbers/Cyclic/Int31/Cyclic31.v2
-rw-r--r--theories/Numbers/Cyclic/Int31/Int31.v2
-rw-r--r--theories/Numbers/Cyclic/ZModulo/ZModulo.v6
3 files changed, 5 insertions, 5 deletions
diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v
index 4b0bda3d44..a7bc4211ed 100644
--- a/theories/Numbers/Cyclic/Int31/Cyclic31.v
+++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v
@@ -1288,7 +1288,7 @@ Section Int31_Specs.
intros; rewrite <- spec_1; apply spec_add.
Qed.
- (** Substraction *)
+ (** Subtraction *)
Lemma spec_sub_c : forall x y, [-|sub31c x y|] = [|x|] - [|y|].
Proof.
diff --git a/theories/Numbers/Cyclic/Int31/Int31.v b/theories/Numbers/Cyclic/Int31/Int31.v
index b9185c9ca0..10f819b005 100644
--- a/theories/Numbers/Cyclic/Int31/Int31.v
+++ b/theories/Numbers/Cyclic/Int31/Int31.v
@@ -255,7 +255,7 @@ Definition add31carryc (n m : int31) :=
| _ => C1 npmpone
end.
-(** * Substraction *)
+(** * Subtraction *)
(** Subtraction modulo [2^31] *)
diff --git a/theories/Numbers/Cyclic/ZModulo/ZModulo.v b/theories/Numbers/Cyclic/ZModulo/ZModulo.v
index 4bcd22543f..94da55b3f3 100644
--- a/theories/Numbers/Cyclic/ZModulo/ZModulo.v
+++ b/theories/Numbers/Cyclic/ZModulo/ZModulo.v
@@ -372,7 +372,7 @@ Section ZModulo.
assert (Z.div_eucl ([|x|]*[|y|]) wB = (([|x|]*[|y|])/wB,([|x|]*[|y|]) mod wB)).
unfold Z.modulo, Z.div; destruct Z.div_eucl; auto.
generalize (Z_div_mod ([|x|]*[|y|]) wB wB_pos); destruct Z.div_eucl as (h,l).
- destruct 1; injection H as ? ?.
+ destruct 1; injection H as [= ? ?].
rewrite H0.
assert ([|l|] = l).
apply Zmod_small; auto.
@@ -414,7 +414,7 @@ Section ZModulo.
unfold Z.modulo, Z.div; destruct Z.div_eucl; auto.
generalize (Z_div_mod [|a|] [|b|] H0).
destruct Z.div_eucl as (q,r); destruct 1; intros.
- injection H1 as ? ?.
+ injection H1 as [= ? ?].
assert ([|r|]=r).
apply Zmod_small; generalize (Z_mod_lt b wB wB_pos); fold [|b|];
auto with zarith.
@@ -525,7 +525,7 @@ Section ZModulo.
unfold Z.modulo, Z.div; destruct Z.div_eucl; auto.
generalize (Z_div_mod a [|b|] H3).
destruct Z.div_eucl as (q,r); destruct 1; intros.
- injection H4 as ? ?.
+ injection H4 as [= ? ?].
assert ([|r|]=r).
apply Zmod_small; generalize (Z_mod_lt b wB wB_pos); fold [|b|];
auto with zarith.