diff options
Diffstat (limited to 'theories/Numbers/Cyclic')
| -rw-r--r-- | theories/Numbers/Cyclic/Int31/Cyclic31.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Cyclic/Int31/Int31.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Cyclic/ZModulo/ZModulo.v | 6 |
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. |
