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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-03-28 22:16:14 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-03-28 22:16:14 +0000
commitb730066fb4dfdeccd7b17538eda845d0048c68ca (patch)
tree25e10bc3b9780ded7cbc6e7c27dc0c0993f966f0 /theories/Reals/Ranalysis1.v
parent98af1982684a02f9521d28594e0fa01ac3275083 (diff)
Nommage explicite de certains "intro" pour préserver la compatibilité
en préparation du passage à des inductifs à polymorphisme de sorte ("sigT R" va devenir de type le type de R, càd Set) git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8670 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Ranalysis1.v')
-rw-r--r--theories/Reals/Ranalysis1.v28
1 files changed, 14 insertions, 14 deletions
diff --git a/theories/Reals/Ranalysis1.v b/theories/Reals/Ranalysis1.v
index fce508f18..5751f843c 100644
--- a/theories/Reals/Ranalysis1.v
+++ b/theories/Reals/Ranalysis1.v
@@ -453,7 +453,7 @@ Qed.
Theorem derivable_continuous_pt :
forall f (x:R), derivable_pt f x -> continuity_pt f x.
-intros.
+intros f x X.
generalize (derivable_derive f x X); intro.
elim H; intros l H1.
cut (l = fct_cte l x).
@@ -468,7 +468,7 @@ unfold fct_cte in |- *; reflexivity.
Qed.
Theorem derivable_continuous : forall f, derivable f -> continuity f.
-unfold derivable, continuity in |- *; intros.
+unfold derivable, continuity in |- *; intros f X x.
apply (derivable_continuous_pt f x (X x)).
Qed.
@@ -661,7 +661,7 @@ Qed.
Lemma derivable_pt_plus :
forall f1 f2 (x:R),
derivable_pt f1 x -> derivable_pt f2 x -> derivable_pt (f1 + f2) x.
-unfold derivable_pt in |- *; intros.
+unfold derivable_pt in |- *; intros f1 f2 x X X0.
elim X; intros.
elim X0; intros.
apply existT with (x0 + x1).
@@ -670,7 +670,7 @@ Qed.
Lemma derivable_pt_opp :
forall f (x:R), derivable_pt f x -> derivable_pt (- f) x.
-unfold derivable_pt in |- *; intros.
+unfold derivable_pt in |- *; intros f x X.
elim X; intros.
apply existT with (- x0).
apply derivable_pt_lim_opp; assumption.
@@ -679,7 +679,7 @@ Qed.
Lemma derivable_pt_minus :
forall f1 f2 (x:R),
derivable_pt f1 x -> derivable_pt f2 x -> derivable_pt (f1 - f2) x.
-unfold derivable_pt in |- *; intros.
+unfold derivable_pt in |- *; intros f1 f2 x X X0.
elim X; intros.
elim X0; intros.
apply existT with (x0 - x1).
@@ -689,7 +689,7 @@ Qed.
Lemma derivable_pt_mult :
forall f1 f2 (x:R),
derivable_pt f1 x -> derivable_pt f2 x -> derivable_pt (f1 * f2) x.
-unfold derivable_pt in |- *; intros.
+unfold derivable_pt in |- *; intros f1 f2 x X X0.
elim X; intros.
elim X0; intros.
apply existT with (x0 * f2 x + f1 x * x1).
@@ -704,7 +704,7 @@ Qed.
Lemma derivable_pt_scal :
forall f (a x:R), derivable_pt f x -> derivable_pt (mult_real_fct a f) x.
-unfold derivable_pt in |- *; intros.
+unfold derivable_pt in |- *; intros f1 a x X.
elim X; intros.
apply existT with (a * x0).
apply derivable_pt_lim_scal; assumption.
@@ -724,7 +724,7 @@ Qed.
Lemma derivable_pt_comp :
forall f1 f2 (x:R),
derivable_pt f1 x -> derivable_pt f2 (f1 x) -> derivable_pt (f2 o f1) x.
-unfold derivable_pt in |- *; intros.
+unfold derivable_pt in |- *; intros f1 f2 x X X0.
elim X; intros.
elim X0; intros.
apply existT with (x1 * x0).
@@ -733,24 +733,24 @@ Qed.
Lemma derivable_plus :
forall f1 f2, derivable f1 -> derivable f2 -> derivable (f1 + f2).
-unfold derivable in |- *; intros.
+unfold derivable in |- *; intros f1 f2 X X0 x.
apply (derivable_pt_plus _ _ x (X _) (X0 _)).
Qed.
Lemma derivable_opp : forall f, derivable f -> derivable (- f).
-unfold derivable in |- *; intros.
+unfold derivable in |- *; intros f X x.
apply (derivable_pt_opp _ x (X _)).
Qed.
Lemma derivable_minus :
forall f1 f2, derivable f1 -> derivable f2 -> derivable (f1 - f2).
-unfold derivable in |- *; intros.
+unfold derivable in |- *; intros f1 f2 X X0 x.
apply (derivable_pt_minus _ _ x (X _) (X0 _)).
Qed.
Lemma derivable_mult :
forall f1 f2, derivable f1 -> derivable f2 -> derivable (f1 * f2).
-unfold derivable in |- *; intros.
+unfold derivable in |- *; intros f1 f2 X X0 x.
apply (derivable_pt_mult _ _ x (X _) (X0 _)).
Qed.
@@ -761,7 +761,7 @@ Qed.
Lemma derivable_scal :
forall f (a:R), derivable f -> derivable (mult_real_fct a f).
-unfold derivable in |- *; intros.
+unfold derivable in |- *; intros f a X x.
apply (derivable_pt_scal _ a x (X _)).
Qed.
@@ -775,7 +775,7 @@ Qed.
Lemma derivable_comp :
forall f1 f2, derivable f1 -> derivable f2 -> derivable (f2 o f1).
-unfold derivable in |- *; intros.
+unfold derivable in |- *; intros f1 f2 X X0 x.
apply (derivable_pt_comp _ _ x (X _) (X0 _)).
Qed.