diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-05-05 15:13:04 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-05-05 15:13:04 +0000 |
| commit | 959543f6f899f0384394f9770abbf17649f69b81 (patch) | |
| tree | 46dc4791f1799a3b2095bec6d887d9aa54f42ad3 /theories/Reals | |
| parent | d2bd5d87d23d443f6e41496bdfe5f8e82d675634 (diff) | |
BinInt: Z.add become the alternative Z.add'
It relies on Z.pos_sub instead of a Pos.compare followed by Pos.sub.
Proofs seem to be quite easy to adapt, via some rewrite Z.pos_sub_spec.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14107 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals')
| -rw-r--r-- | theories/Reals/RIneq.v | 3 | ||||
| -rw-r--r-- | theories/Reals/Rfunctions.v | 10 |
2 files changed, 8 insertions, 5 deletions
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index de41fd3f6..70f4ff0d9 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -1717,7 +1717,8 @@ Qed. Lemma plus_IZR_NEG_POS : forall p q:positive, IZR (Zpos p + Zneg q) = IZR (Zpos p) + IZR (Zneg q). Proof. - intros p q; simpl. case Pcompare_spec; intros H; simpl. + intros p q; simpl. rewrite Z.pos_sub_spec. + case Pcompare_spec; intros H; simpl. subst. ring. rewrite Pminus_minus by trivial. rewrite minus_INR by (now apply lt_le_weak, Plt_lt). diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v index 1eee8d852..c0cd78649 100644 --- a/theories/Reals/Rfunctions.v +++ b/theories/Reals/Rfunctions.v @@ -557,6 +557,7 @@ Proof. (* POS/POS *) rewrite Pplus_plus; auto with real. (* POS/NEG *) + rewrite Z.pos_sub_spec. case Pcompare_spec; intros; simpl. subst; auto with real. rewrite Pminus_minus by trivial. @@ -568,16 +569,17 @@ Proof. rewrite plus_comm, le_plus_minus_r by (now apply lt_le_weak, Plt_lt). reflexivity. (* NEG/POS *) + rewrite Z.pos_sub_spec. case Pcompare_spec; intros; simpl. subst; auto with real. rewrite Pminus_minus by trivial. - rewrite (pow_RN_plus x _ (nat_of_P n1)) by auto with real. - rewrite plus_comm, le_plus_minus_r by (now apply lt_le_weak, Plt_lt). - auto with real. - rewrite Pminus_minus by trivial. rewrite (pow_RN_plus x _ (nat_of_P m1)) by auto with real. rewrite plus_comm, le_plus_minus_r by (now apply lt_le_weak, Plt_lt). rewrite Rinv_mult_distr, Rinv_involutive; auto with real. + rewrite Pminus_minus by trivial. + rewrite (pow_RN_plus x _ (nat_of_P n1)) by auto with real. + rewrite plus_comm, le_plus_minus_r by (now apply lt_le_weak, Plt_lt). + auto with real. (* NEG/NEG *) rewrite Pplus_plus; auto with real. intros H'; rewrite pow_add; auto with real. |