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| author |  desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-22 13:39:23 +0000 |
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| committer | desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-22 13:39:23 +0000 |
| commit | b5e03cd4521fa470e04ad552b401f250a99ae09c (patch) | |
| tree | 51a9132728854a1271d34dbfe4cc221a7d3fbdba /theories/Reals/RiemannInt.v | |
| parent | 126143a69589f397b7485f111a0edcb51f03589c (diff) | |
Renommages dans Rcomplete
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3578 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/RiemannInt.v')
| -rw-r--r-- | theories/Reals/RiemannInt.v | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/theories/Reals/RiemannInt.v b/theories/Reals/RiemannInt.v index 5ea7268f2..8a4379a83 100644 --- a/theories/Reals/RiemannInt.v +++ b/theories/Reals/RiemannInt.v @@ -42,7 +42,7 @@ Apply H1. Qed. Lemma RiemannInt_P2 : (f:R->R;a,b:R;un:nat->posreal;vn,wn:nat->(StepFun a b)) (Un_cv un R0) -> ``a<=b`` -> ((n:nat)((t:R)``(Rmin a b)<=t<=(Rmax a b)``->``(Rabsolu ((f t)-(vn n t)))<=(wn n t)``)/\``(Rabsolu (RiemannInt_SF (wn n)))<(un n)``) -> (sigTT ? [l:R](Un_cv [N:nat](RiemannInt_SF (vn N)) l)). -Intros; Apply R_complet; Unfold Un_cv in H; Unfold Cauchy_crit; Intros; Assert H3 : ``0<eps/2``. +Intros; Apply R_complete; Unfold Un_cv in H; Unfold Cauchy_crit; Intros; Assert H3 : ``0<eps/2``. Unfold Rdiv; Apply Rmult_lt_pos; [Assumption | Apply Rlt_Rinv; Sup0]. Elim (H ? H3); Intros N0 H4; Exists N0; Intros; Unfold R_dist; Unfold R_dist in H4; Elim (H1 n); Elim (H1 m); Intros; Replace ``(RiemannInt_SF (vn n))-(RiemannInt_SF (vn m))`` with ``(RiemannInt_SF (vn n))+(-1)*(RiemannInt_SF (vn m))``; [Idtac | Ring]; Rewrite <- StepFun_P30; Apply Rle_lt_trans with (RiemannInt_SF (mkStepFun (StepFun_P32 (mkStepFun (StepFun_P28 ``-1`` (vn n) (vn m)))))). Apply StepFun_P34; Assumption. |