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authorGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
committerGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
commit61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch)
tree961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Reals/Ranalysis.v
parent6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (diff)
Delete trailing whitespaces in all *.{v,ml*} files
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Ranalysis.v')
-rw-r--r--theories/Reals/Ranalysis.v24
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/Reals/Ranalysis.v b/theories/Reals/Ranalysis.v
index 371c1af74..500dd5295 100644
--- a/theories/Reals/Ranalysis.v
+++ b/theories/Reals/Ranalysis.v
@@ -85,7 +85,7 @@ Ltac intro_hyp_glob trm :=
match goal with
| _:(forall x0:R, aux x0 <> 0) |- (derivable _) =>
intro_hyp_glob X1
- | _:(forall x0:R, aux x0 <> 0) |- (continuity _) =>
+ | _:(forall x0:R, aux x0 <> 0) |- (continuity _) =>
intro_hyp_glob X1
| |- (derivable _) =>
cut (forall x0:R, aux x0 <> 0);
@@ -277,7 +277,7 @@ Ltac intro_hyp_pt trm pt :=
Ltac is_diff_pt :=
match goal with
| |- (derivable_pt Rsqr _) =>
-
+
(* fonctions de base *)
apply derivable_pt_Rsqr
| |- (derivable_pt id ?X1) => apply (derivable_pt_id X1)
@@ -326,7 +326,7 @@ Ltac is_diff_pt :=
unfold plus_fct, mult_fct, div_fct, minus_fct, opp_fct, inv_fct,
comp, pow_fct, id, fct_cte in |- * ]
| |- (derivable_pt (/ ?X1) ?X2) =>
-
+
(* INVERSION *)
apply (derivable_pt_inv X1 X2);
[ assumption ||
@@ -334,7 +334,7 @@ Ltac is_diff_pt :=
comp, pow_fct, id, fct_cte in |- *
| is_diff_pt ]
| |- (derivable_pt (comp ?X1 ?X2) ?X3) =>
-
+
(* COMPOSITION *)
apply (derivable_pt_comp X2 X1 X3); is_diff_pt
| _:(derivable_pt ?X1 ?X2) |- (derivable_pt ?X1 ?X2) =>
@@ -352,7 +352,7 @@ Ltac is_diff_pt :=
(**********)
Ltac is_diff_glob :=
match goal with
- | |- (derivable Rsqr) =>
+ | |- (derivable Rsqr) =>
(* fonctions de base *)
apply derivable_Rsqr
| |- (derivable id) => apply derivable_id
@@ -392,7 +392,7 @@ Ltac is_diff_glob :=
unfold plus_fct, mult_fct, div_fct, minus_fct, opp_fct, inv_fct,
id, fct_cte, comp, pow_fct in |- * ]
| |- (derivable (/ ?X1)) =>
-
+
(* INVERSION *)
apply (derivable_inv X1);
[ try
@@ -401,7 +401,7 @@ Ltac is_diff_glob :=
id, fct_cte, comp, pow_fct in |- *
| is_diff_glob ]
| |- (derivable (comp sqrt _)) =>
-
+
(* COMPOSITION *)
unfold derivable in |- *; intro; try is_diff_pt
| |- (derivable (comp Rabs _)) =>
@@ -421,7 +421,7 @@ Ltac is_diff_glob :=
Ltac is_cont_pt :=
match goal with
| |- (continuity_pt Rsqr _) =>
-
+
(* fonctions de base *)
apply derivable_continuous_pt; apply derivable_pt_Rsqr
| |- (continuity_pt id ?X1) =>
@@ -475,7 +475,7 @@ Ltac is_cont_pt :=
unfold plus_fct, mult_fct, div_fct, minus_fct, opp_fct, inv_fct,
comp, id, fct_cte, pow_fct in |- * ]
| |- (continuity_pt (/ ?X1) ?X2) =>
-
+
(* INVERSION *)
apply (continuity_pt_inv X1 X2);
[ is_cont_pt
@@ -483,7 +483,7 @@ Ltac is_cont_pt :=
unfold plus_fct, mult_fct, div_fct, minus_fct, opp_fct, inv_fct,
comp, id, fct_cte, pow_fct in |- * ]
| |- (continuity_pt (comp ?X1 ?X2) ?X3) =>
-
+
(* COMPOSITION *)
apply (continuity_pt_comp X2 X1 X3); is_cont_pt
| _:(continuity_pt ?X1 ?X2) |- (continuity_pt ?X1 ?X2) =>
@@ -508,7 +508,7 @@ Ltac is_cont_pt :=
Ltac is_cont_glob :=
match goal with
| |- (continuity Rsqr) =>
-
+
(* fonctions de base *)
apply derivable_continuous; apply derivable_Rsqr
| |- (continuity id) => apply derivable_continuous; apply derivable_id
@@ -559,7 +559,7 @@ Ltac is_cont_glob :=
unfold plus_fct, mult_fct, div_fct, minus_fct, opp_fct, inv_fct,
id, fct_cte, pow_fct in |- * ]
| |- (continuity (comp sqrt _)) =>
-
+
(* COMPOSITION *)
unfold continuity_pt in |- *; intro; try is_cont_pt
| |- (continuity (comp ?X1 ?X2)) =>