diff options
Diffstat (limited to 'src/Algebra/Monoid.v')
| -rw-r--r-- | src/Algebra/Monoid.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/src/Algebra/Monoid.v b/src/Algebra/Monoid.v index 565058cf7..bd15290c7 100644 --- a/src/Algebra/Monoid.v +++ b/src/Algebra/Monoid.v @@ -11,7 +11,7 @@ Section Monoid. Lemma cancel_right z iz (Hinv:op z iz = id) : forall x y, x * z = y * z <-> x = y. - Proof. + Proof using Type*. split; intros. { assert (op (op x z) iz = op (op y z) iz) as Hcut by (rewrite_hyp ->!*; reflexivity). rewrite <-associative in Hcut. @@ -21,7 +21,7 @@ Section Monoid. Lemma cancel_left z iz (Hinv:op iz z = id) : forall x y, z * x = z * y <-> x = y. - Proof. + Proof using Type*. split; intros. { assert (op iz (op z x) = op iz (op z y)) as Hcut by (rewrite_hyp ->!*; reflexivity). rewrite !associative, !Hinv, !left_identity in Hcut; exact Hcut. } @@ -29,14 +29,14 @@ Section Monoid. Qed. Lemma inv_inv x ix iix : ix*x = id -> iix*ix = id -> iix = x. - Proof. + Proof using Type*. intros Hi Hii. assert (H:op iix id = op iix (op ix x)) by (rewrite Hi; reflexivity). rewrite associative, Hii, left_identity, right_identity in H; exact H. Qed. Lemma inv_op x y ix iy : ix*x = id -> iy*y = id -> (iy*ix)*(x*y) =id. - Proof. + Proof using Type*. intros Hx Hy. cut (iy * (ix*x) * y = id); try intro H. { rewrite <-!associative; rewrite <-!associative in H; exact H. } |