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.

Lemma five_segment a a' b b' c c' d d' :
cong a b a' b' -> cong b c b' c' -> cong a d a' d' -> cong b d b' d' ->
bet a b c -> bet a' b' c' -> a <> b -> cong c d c' d'.