diff options
Diffstat (limited to 'theories/Numbers/NatInt')
| -rw-r--r-- | theories/Numbers/NatInt/NZAxioms.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/NatInt/NZMulOrder.v | 4 |
2 files changed, 3 insertions, 3 deletions
diff --git a/theories/Numbers/NatInt/NZAxioms.v b/theories/Numbers/NatInt/NZAxioms.v index fcd98787f9..ef68c3bca7 100644 --- a/theories/Numbers/NatInt/NZAxioms.v +++ b/theories/Numbers/NatInt/NZAxioms.v @@ -43,7 +43,7 @@ End IsNZDomain. (** Axiomatization of some more constants Simply denoting "1" for (S 0) and so on works ok when implementing - by nat, but leaves some (Nsucc N0) when implementing by N. + by nat, but leaves some (N.succ N0) when implementing by N. *) Module Type OneTwo (Import T:Typ). diff --git a/theories/Numbers/NatInt/NZMulOrder.v b/theories/Numbers/NatInt/NZMulOrder.v index 97306f9340..f6de98560e 100644 --- a/theories/Numbers/NatInt/NZMulOrder.v +++ b/theories/Numbers/NatInt/NZMulOrder.v @@ -271,9 +271,9 @@ Definition mul_eq_0 := eq_mul_0. Definition mul_eq_0_l := eq_mul_0_l. Definition mul_eq_0_r := eq_mul_0_r. -Theorem lt_0_mul : forall n m, 0 < n * m <-> (0 < n /\ 0 < m) \/ (m < 0 /\ n < 0). +Theorem lt_0_mul n m : 0 < n * m <-> (0 < n /\ 0 < m) \/ (m < 0 /\ n < 0). Proof. -intros n m; split; [intro H | intros [[H1 H2] | [H1 H2]]]. +split; [intro H | intros [[H1 H2] | [H1 H2]]]. destruct (lt_trichotomy n 0) as [H1 | [H1 | H1]]; [| rewrite H1 in H; rewrite mul_0_l in H; false_hyp H lt_irrefl |]; (destruct (lt_trichotomy m 0) as [H2 | [H2 | H2]]; |