diff options
Diffstat (limited to 'theories/ZArith/Zsqrt_def.v')
| -rw-r--r-- | theories/ZArith/Zsqrt_def.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/ZArith/Zsqrt_def.v b/theories/ZArith/Zsqrt_def.v index 824a447c2c..b3d1fa1ebf 100644 --- a/theories/ZArith/Zsqrt_def.v +++ b/theories/ZArith/Zsqrt_def.v @@ -8,7 +8,7 @@ (** Definition of a square root function for Z. *) -Require Import BinPos BinInt Psqrt. +Require Import BinPos BinInt. Local Open Scope Z_scope. @@ -16,7 +16,7 @@ Definition Zsqrtrem n := match n with | 0 => (0, 0) | Zpos p => - match Psqrtrem p with + match Pos.sqrtrem p with | (s, IsPos r) => (Zpos s, Zpos r) | (s, _) => (Zpos s, 0) end @@ -26,7 +26,7 @@ Definition Zsqrtrem n := Definition Zsqrt n := match n with | 0 => 0 - | Zpos p => Zpos (Psqrt p) + | Zpos p => Zpos (Pos.sqrt p) | Zneg _ => 0 end. @@ -34,7 +34,7 @@ Lemma Zsqrtrem_spec : forall n, 0<=n -> let (s,r) := Zsqrtrem n in n = s*s + r /\ 0 <= r <= 2*s. Proof. destruct n. now repeat split. - generalize (Psqrtrem_spec p). simpl. + generalize (Pos.sqrtrem_spec p). simpl. destruct 1; simpl; subst; now repeat split. now destruct 1. Qed. @@ -43,7 +43,7 @@ Lemma Zsqrt_spec : forall n, 0<=n -> let s := Zsqrt n in s*s <= n < (Zsucc s)*(Zsucc s). Proof. destruct n. now repeat split. unfold Zsqrt. - rewrite <- Zpos_succ_morphism. intros _. apply (Psqrt_spec p). + rewrite <- Zpos_succ_morphism. intros _. apply (Pos.sqrt_spec p). now destruct 1. Qed. @@ -55,6 +55,6 @@ Qed. Lemma Zsqrtrem_sqrt : forall n, fst (Zsqrtrem n) = Zsqrt n. Proof. destruct n; try reflexivity. - unfold Zsqrtrem, Zsqrt, Psqrt. - destruct (Psqrtrem p) as (s,r). now destruct r. + unfold Zsqrtrem, Zsqrt, Pos.sqrt. + destruct (Pos.sqrtrem p) as (s,r). now destruct r. Qed.
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