diff options
Diffstat (limited to 'theories/Numbers/Natural/Binary')
| -rw-r--r-- | theories/Numbers/Natural/Binary/NBinDefs.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Numbers/Natural/Binary/NBinDefs.v b/theories/Numbers/Natural/Binary/NBinDefs.v index 268879aa4d..e0f3fdf4bb 100644 --- a/theories/Numbers/Natural/Binary/NBinDefs.v +++ b/theories/Numbers/Natural/Binary/NBinDefs.v @@ -12,7 +12,7 @@ Require Import BinPos. Require Export BinNat. -Require Import NMinus. +Require Import NSub. Open Local Scope N_scope. @@ -28,7 +28,7 @@ Definition NZ0 := N0. Definition NZsucc := Nsucc. Definition NZpred := Npred. Definition NZadd := Nplus. -Definition NZminus := Nminus. +Definition NZsub := Nminus. Definition NZmul := Nmult. Theorem NZeq_equiv : equiv N NZeq. @@ -55,7 +55,7 @@ Proof. congruence. Qed. -Add Morphism NZminus with signature NZeq ==> NZeq ==> NZeq as NZminus_wd. +Add Morphism NZsub with signature NZeq ==> NZeq ==> NZeq as NZsub_wd. Proof. congruence. Qed. @@ -93,12 +93,12 @@ simpl in |- *; reflexivity. simpl in |- *; rewrite Pplus_succ_permute_l; reflexivity. Qed. -Theorem NZminus_0_r : forall n : NZ, n - N0 = n. +Theorem NZsub_0_r : forall n : NZ, n - N0 = n. Proof. now destruct n. Qed. -Theorem NZminus_succ_r : forall n m : NZ, n - (NZsucc m) = NZpred (n - m). +Theorem NZsub_succ_r : forall n m : NZ, n - (NZsucc m) = NZpred (n - m). Proof. destruct n as [| p]; destruct m as [| q]; try reflexivity. now destruct p. @@ -242,7 +242,7 @@ Qed. End NBinaryAxiomsMod. -Module Export NBinaryMinusPropMod := NMinusPropFunct NBinaryAxiomsMod. +Module Export NBinarySubPropMod := NSubPropFunct NBinaryAxiomsMod. (* Some fun comparing the efficiency of the generic log defined by strong (course-of-value) recursion and the log defined by recursion |