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| author |  Stephane Glondu <steph@glondu.net> | 2010-07-21 09:46:51 +0200 |
|---|---|---|
| committer | Stephane Glondu <steph@glondu.net> | 2010-07-21 09:46:51 +0200 |
| commit | 5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 (patch) | |
| tree | 631ad791a7685edafeb1fb2e8faeedc8379318ae /theories/Reals/Rgeom.v | |
| parent | da178a880e3ace820b41d38b191d3785b82991f5 (diff) | |
Imported Upstream snapshot 8.3~beta0+13298
Diffstat (limited to 'theories/Reals/Rgeom.v')
| -rw-r--r-- | theories/Reals/Rgeom.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Reals/Rgeom.v b/theories/Reals/Rgeom.v index c96ae5d6..8890cbb5 100644 --- a/theories/Reals/Rgeom.v +++ b/theories/Reals/Rgeom.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Rgeom.v 10710 2008-03-23 09:24:09Z herbelin $ i*) +(*i $Id$ i*) Require Import Rbase. Require Import Rfunctions. @@ -32,7 +32,7 @@ Proof. Qed. Lemma distance_symm : - forall x0 y0 x1 y1:R, dist_euc x0 y0 x1 y1 = dist_euc x1 y1 x0 y0. + forall x0 y0 x1 y1:R, dist_euc x0 y0 x1 y1 = dist_euc x1 y1 x0 y0. Proof. intros x0 y0 x1 y1; unfold dist_euc in |- *; apply Rsqr_inj; [ apply sqrt_positivity; apply Rplus_le_le_0_compat @@ -187,7 +187,7 @@ Lemma isometric_rot_trans : forall x1 y1 x2 y2 tx ty theta:R, Rsqr (x1 - x2) + Rsqr (y1 - y2) = Rsqr (xr (xt x1 tx) (yt y1 ty) theta - xr (xt x2 tx) (yt y2 ty) theta) + - Rsqr (yr (xt x1 tx) (yt y1 ty) theta - yr (xt x2 tx) (yt y2 ty) theta). + Rsqr (yr (xt x1 tx) (yt y1 ty) theta - yr (xt x2 tx) (yt y2 ty) theta). Proof. intros; rewrite <- isometric_rotation_0; apply isometric_translation. Qed. @@ -196,7 +196,7 @@ Lemma isometric_trans_rot : forall x1 y1 x2 y2 tx ty theta:R, Rsqr (x1 - x2) + Rsqr (y1 - y2) = Rsqr (xt (xr x1 y1 theta) tx - xt (xr x2 y2 theta) tx) + - Rsqr (yt (yr x1 y1 theta) ty - yt (yr x2 y2 theta) ty). + Rsqr (yt (yr x1 y1 theta) ty - yt (yr x2 y2 theta) ty). Proof. intros; rewrite <- isometric_translation; apply isometric_rotation_0. Qed. |