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 inner_pasch a b c p q :
bet a p c -> bet b q c ->
a <> p -> p <> c -> b <> q -> q <> c ->
~ (bet a b c \/ bet b c a \/ bet c a b) ->
exists x, bet p x b /\ bet q x a.