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 markov_betE a b c :
~ ~ [ /\ [ \/ a 0 0 != b 0 0 | a 0 1 != b 0 1 ] &
[ \/ b 0 0 != c 0 0 | b 0 1 != c 0 1 ] ] ->
[ /\ [ \/ a 0 0 != b 0 0 | a 0 1 != b 0 1 ] &
[ \/ b 0 0 != c 0 0 | b 0 1 != c 0 1 ] ].