Definition contraction a b k := k *: (b - a) + a.

Lemma inner_pasch' a b c p q (k1 := betR a p c) (k2 := betR b q c) :
a <> p -> p <> c -> b <> q -> q <> c ->
bet a p c -> bet b q c ->
exists x, bet p x b /\ bet q x a.