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| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-01-04 18:48:06 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-01-04 18:48:06 +0000 |
| commit | 12c796fe185876021e2dfc7753b8f90ba9de31e0 (patch) | |
| tree | 38eea7388cb9295f2169ad34eb1682578017aaee /theories/ZArith | |
| parent | fdda04b92b7347f252d41aa76693ec221a07fe47 (diff) | |
Ndigits: a Pshiftl_nat used in BigN (was double_digits there)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13764 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith')
| -rw-r--r-- | theories/ZArith/Zdigits_def.v | 16 |
1 files changed, 16 insertions, 0 deletions
diff --git a/theories/ZArith/Zdigits_def.v b/theories/ZArith/Zdigits_def.v index 028149eb8..618214357 100644 --- a/theories/ZArith/Zdigits_def.v +++ b/theories/ZArith/Zdigits_def.v @@ -418,3 +418,19 @@ Proof. now rewrite Nxor_spec, negb_xorb_l. now rewrite Nxor_spec, xorb_negb_negb. Qed. + +(** An additionnal proof concerning [Pshiftl_nat], used in BigN *) + +Lemma Pshiftl_nat_Zpower : forall n p, + Zpos (Pshiftl_nat p n) = Zpos p * 2 ^ Z_of_nat n. +Proof. + intros. + rewrite Zmult_comm. + induction n. simpl; auto. + transitivity (2 * (2 ^ Z_of_nat n * Zpos p)). + rewrite <- IHn. auto. + rewrite Zmult_assoc. + rewrite inj_S. + rewrite <- Zpower_succ_r; auto with zarith. + apply Zle_0_nat. +Qed. |