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| author |  desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-07-16 09:02:39 +0000 |
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| committer | desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-07-16 09:02:39 +0000 |
| commit | 1e558a3ce46468154c719eba3f6812be23ab49d7 (patch) | |
| tree | 32e98c4344acba472f2099239787086cd2400325 /theories/Reals/Ranalysis4.v | |
| parent | 62c194585824256fa8f5967e079388c8d2e703ad (diff) | |
*** empty log message ***
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2879 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Ranalysis4.v')
| -rw-r--r-- | theories/Reals/Ranalysis4.v | 16 |
1 files changed, 16 insertions, 0 deletions
diff --git a/theories/Reals/Ranalysis4.v b/theories/Reals/Ranalysis4.v index a3ce1e4d1..afd65a500 100644 --- a/theories/Reals/Ranalysis4.v +++ b/theories/Reals/Ranalysis4.v @@ -16,9 +16,25 @@ Require Rderiv. Require DiscrR. Require Rtrigo. Require Ranalysis1. +Require R_sqrt. Require Ranalysis2. Require Ranalysis3. +(* sqrt *) +Axiom derivable_pt_lim_sqrt : (x:R) ``0<x`` -> (derivable_pt_lim sqrt x ``/(2*(sqrt x))``). + +Lemma derivable_pt_sqrt : (x:R) ``0<x`` -> (derivable_pt sqrt x). +Unfold derivable_pt; Intros. +Apply Specif.existT with ``/(2*(sqrt x))``. +Apply derivable_pt_lim_sqrt; Assumption. +Qed. + +Lemma derive_pt_sqrt : (x:R;pr:``0<x``) ``(derive_pt sqrt x (derivable_pt_sqrt ? pr)) == /(2*(sqrt x))``. +Intros. +Apply derive_pt_eq_0. +Apply derivable_pt_lim_sqrt; Assumption. +Qed. + (**********) Lemma derivable_pt_inv : (f:R->R;x:R) ``(f x)<>0`` -> (derivable_pt f x) -> (derivable_pt (inv_fct f) x). Intros; Cut (derivable_pt (div_fct (fct_cte R1) f) x) -> (derivable_pt (inv_fct f) x). |