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(** *                       Similarity                            *)
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(* Specifications: *)
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).
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).