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Diffstat (limited to 'theories/ZArith/BinInt.v')
| -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. |