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.

Lemma bet_ratio a b k1 : 0 < k1 -> k1 < 1 -> bet a b (k1^-1 *: (b - a) + a).
Definition extension a b k := k^-1 *: (b - a) + a.