Section TarskiGe1.
Variable R : realFieldType.
Variable n : nat.
Implicit Types (a b c d : (@ Vector R n)).
Definition cong a b c d := (b - a) *m (b - a)^T == (d - c) *m (d - c)^T.
Definition bet a b c := betE a b c || betS a b c.
Definition extension a b k := k^-1 *: (b - a) + a.
Definition contraction a b k := k *: (b - a) + a.
Definition sqr_L2_norm_2D a b :=
(b 0 0 - a 0 0) ^+ 2 + (b 0 1 - a 0 1) ^+ 2.

Lemma ratioP_aux (v1 v2 : 'rV[R]_(2)) :
v1 0 0 != 0 -> v1 0 1 != 0 -> v2 0 0 != 0 -> v2 0 1 != 0 ->
v1 0 0 * v2 0 1 == v1 0 1 * v2 0 0 -> ratio v1 v2 = v1 0 0 / v2 0 0.