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-rw-r--r--contrib/ring/Ring_theory.v18
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.