diff options
| author |  Hugo Herbelin <Hugo.Herbelin@inria.fr> | 2017-03-03 10:27:30 +0100 |
|---|---|---|
| committer | Hugo Herbelin <Hugo.Herbelin@inria.fr> | 2017-03-03 10:45:03 +0100 |
| commit | 27d92355d38af5ee93c7343a62671701e72c1096 (patch) | |
| tree | 9e813c3be24378b2c266d309c5fb910a7ddc7a99 /theories | |
| parent | a61494c8c430477da8a4b3367a8ac5d492bf83c1 (diff) | |
Completing basic lemmas about <= and < in BinInt.Z.Pos2Z.
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/ZArith/BinInt.v | 15 |
1 files changed, 15 insertions, 0 deletions
diff --git a/theories/ZArith/BinInt.v b/theories/ZArith/BinInt.v index d09337484..1e3ab6687 100644 --- a/theories/ZArith/BinInt.v +++ b/theories/ZArith/BinInt.v @@ -1396,6 +1396,21 @@ Proof. easy. Qed. Lemma neg_le_pos p q : Zneg p <= Zpos q. Proof. easy. Qed. +Lemma neg_lt_pos p q : Zneg p < Zpos q. +Proof. easy. Qed. + +Lemma neg_le_neg p q : (q <= p)%positive -> Zneg p <= Zneg q. +Proof. intros; unfold Z.le; simpl. now rewrite <- Pos.compare_antisym. Qed. + +Lemma neg_lt_neg p q : (q < p)%positive -> Zneg p < Zneg q. +Proof. intros; unfold Z.lt; simpl. now rewrite <- Pos.compare_antisym. Qed. + +Lemma pos_le_pos p q : (p <= q)%positive -> Zpos p <= Zpos q. +Proof. easy. Qed. + +Lemma pos_lt_pos p q : (p < q)%positive -> Zpos p < Zpos q. +Proof. easy. Qed. + Lemma neg_xO p : Z.neg p~0 = 2 * Z.neg p. Proof. reflexivity. Qed. |