diff options
Diffstat (limited to 'contrib/ring/Ring_theory.v')
-rw-r--r-- | contrib/ring/Ring_theory.v | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/contrib/ring/Ring_theory.v b/contrib/ring/Ring_theory.v index 31cc274b2..192ff1f57 100644 --- a/contrib/ring/Ring_theory.v +++ b/contrib/ring/Ring_theory.v @@ -39,7 +39,7 @@ Record Semi_Ring_Theory : Prop := SR_mult_one_left : forall n:A, 1 * n = n; SR_mult_zero_left : forall n:A, 0 * n = 0; SR_distr_left : forall n m p:A, (n + m) * p = n * p + m * p; - SR_plus_reg_left : forall n m p:A, n + m = n + p -> m = p; +(* SR_plus_reg_left : forall n m p:A, n + m = n + p -> m = p;*) SR_eq_prop : forall x y:A, Is_true (Aeq x y) -> x = y}. Variable T : Semi_Ring_Theory. @@ -52,10 +52,10 @@ Let plus_zero_left := SR_plus_zero_left T. Let mult_one_left := SR_mult_one_left T. Let mult_zero_left := SR_mult_zero_left T. Let distr_left := SR_distr_left T. -Let plus_reg_left := SR_plus_reg_left T. +(*Let plus_reg_left := SR_plus_reg_left T.*) Hint Resolve plus_comm plus_assoc mult_comm mult_assoc plus_zero_left - mult_one_left mult_zero_left distr_left plus_reg_left. + mult_one_left mult_zero_left distr_left (*plus_reg_left*). (* Lemmas whose form is x=y are also provided in form y=x because Auto does not symmetry *) @@ -126,11 +126,11 @@ Qed. Lemma SR_mult_one_right2 : forall n:A, n = n * 1. intro; elim mult_comm; auto. Qed. - +(* Lemma SR_plus_reg_right : forall n m p:A, m + n = p + n -> m = p. intros n m p; rewrite (plus_comm m n); rewrite (plus_comm p n); eauto. Qed. - +*) End Theory_of_semi_rings. Section Theory_of_rings. @@ -320,7 +320,7 @@ symmetry in |- *; apply Th_mult_opp_opp. Qed. Lemma Th_opp_zero : - 0 = 0. rewrite <- (plus_zero_left (- 0)). auto. Qed. - +(* Lemma Th_plus_reg_left : forall n m p:A, n + m = n + p -> m = p. intros; generalize (f_equal (fun z => - n + z) H). repeat rewrite plus_assoc. @@ -336,7 +336,7 @@ rewrite (plus_comm n m). rewrite (plus_comm n p). auto. Qed. - +*) Lemma Th_distr_right : forall n m p:A, n * (m + p) = n * m + n * p. intros. repeat rewrite (mult_comm n). @@ -349,7 +349,7 @@ Qed. End Theory_of_rings. -Hint Resolve Th_mult_zero_left Th_plus_reg_left: core. +Hint Resolve Th_mult_zero_left (*Th_plus_reg_left*): core. Unset Implicit Arguments. @@ -373,4 +373,4 @@ End product_ring. Section power_ring. -End power_ring.
\ No newline at end of file +End power_ring. |