diff options
Diffstat (limited to 'theories/Numbers/Natural/Binary')
| -rw-r--r-- | theories/Numbers/Natural/Binary/NBinDefs.v | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/theories/Numbers/Natural/Binary/NBinDefs.v b/theories/Numbers/Natural/Binary/NBinDefs.v index 170dfa42f2..268879aa4d 100644 --- a/theories/Numbers/Natural/Binary/NBinDefs.v +++ b/theories/Numbers/Natural/Binary/NBinDefs.v @@ -27,9 +27,9 @@ Definition NZeq := @eq N. Definition NZ0 := N0. Definition NZsucc := Nsucc. Definition NZpred := Npred. -Definition NZplus := Nplus. +Definition NZadd := Nplus. Definition NZminus := Nminus. -Definition NZtimes := Nmult. +Definition NZmul := Nmult. Theorem NZeq_equiv : equiv N NZeq. Proof (eq_equiv N). @@ -50,7 +50,7 @@ Proof. congruence. Qed. -Add Morphism NZplus with signature NZeq ==> NZeq ==> NZeq as NZplus_wd. +Add Morphism NZadd with signature NZeq ==> NZeq ==> NZeq as NZadd_wd. Proof. congruence. Qed. @@ -60,7 +60,7 @@ Proof. congruence. Qed. -Add Morphism NZtimes with signature NZeq ==> NZeq ==> NZeq as NZtimes_wd. +Add Morphism NZmul with signature NZeq ==> NZeq ==> NZeq as NZmul_wd. Proof. congruence. Qed. @@ -79,16 +79,16 @@ case_eq (Psucc p); try (intros q H; rewrite <- H; now rewrite Ppred_succ). intro H; false_hyp H Psucc_not_one. Qed. -Theorem NZplus_0_l : forall n : NZ, N0 + n = n. +Theorem NZadd_0_l : forall n : NZ, N0 + n = n. Proof. reflexivity. Qed. -Theorem NZplus_succ_l : forall n m : NZ, (NZsucc n) + m = NZsucc (n + m). +Theorem NZadd_succ_l : forall n m : NZ, (NZsucc n) + m = NZsucc (n + m). Proof. destruct n; destruct m. simpl in |- *; reflexivity. -unfold NZsucc, NZplus, Nsucc, Nplus. rewrite <- Pplus_one_succ_l; reflexivity. +unfold NZsucc, NZadd, Nsucc, Nplus. rewrite <- Pplus_one_succ_l; reflexivity. simpl in |- *; reflexivity. simpl in |- *; rewrite Pplus_succ_permute_l; reflexivity. Qed. @@ -106,12 +106,12 @@ simpl. rewrite Pminus_mask_succ_r, Pminus_mask_carry_spec. now destruct (Pminus_mask p q) as [| r |]; [| destruct r |]. Qed. -Theorem NZtimes_0_l : forall n : NZ, N0 * n = N0. +Theorem NZmul_0_l : forall n : NZ, N0 * n = N0. Proof. destruct n; reflexivity. Qed. -Theorem NZtimes_succ_l : forall n m : NZ, (NZsucc n) * m = n * m + m. +Theorem NZmul_succ_l : forall n m : NZ, (NZsucc n) * m = n * m + m. Proof. destruct n as [| n]; destruct m as [| m]; simpl; try reflexivity. now rewrite Pmult_Sn_m, Pplus_comm. |