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author | 2002-07-16 09:02:39 +0000 | |
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committer | 2002-07-16 09:02:39 +0000 | |
commit | 1e558a3ce46468154c719eba3f6812be23ab49d7 (patch) | |
tree | 32e98c4344acba472f2099239787086cd2400325 /theories/Reals/Ranalysis1.v | |
parent | 62c194585824256fa8f5967e079388c8d2e703ad (diff) |
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2879 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Ranalysis1.v')
-rw-r--r-- | theories/Reals/Ranalysis1.v | 14 |
1 files changed, 0 insertions, 14 deletions
diff --git a/theories/Reals/Ranalysis1.v b/theories/Reals/Ranalysis1.v index 47397238d..2b919ce65 100644 --- a/theories/Reals/Ranalysis1.v +++ b/theories/Reals/Ranalysis1.v @@ -469,8 +469,6 @@ Elim H6; Intros; Unfold D_x in H10; Elim H10; Intros; Assumption. Elim H6; Intros; Assumption. Qed. -Axiom derivable_pt_lim_sqrt : (x:R) ``0<x`` -> (derivable_pt_lim sqrt x ``/(2*(sqrt x))``). - Axiom derivable_pt_lim_sin : (x:R) (derivable_pt_lim sin x (cos x)). Lemma derivable_pt_lim_cos : (x:R) (derivable_pt_lim cos x ``-(sin x)``). @@ -555,12 +553,6 @@ Apply Specif.existT with ``x1*x0``. Apply derivable_pt_lim_comp; Assumption. Qed. -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 derivable_pt_sin : (x:R) (derivable_pt sin x). Unfold derivable_pt; Intro. Apply Specif.existT with (cos x). @@ -730,12 +722,6 @@ Unfold derive_pt in H0; Rewrite H0 in H4. Apply derivable_pt_lim_comp; 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 derive_pt_sin : (x:R) ``(derive_pt sin x (derivable_pt_sin ?))==(cos x)``. Intros; Apply derive_pt_eq_0. Apply derivable_pt_lim_sin. |