proposition: 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).
proof: Proof. intros; rewrite <- isometric_rotation_0; apply isometric_translation. Qed.
imports: Rbase Rfunctions SeqSeries Rtrigo1 R_sqrt