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

Lemma betEP' a b c :
reflect (~ [ /\ [ \/ a 0 0 != b 0 0 | a 0 1 != b 0 1 ] &
[ \/ b 0 0 != c 0 0 | b 0 1 != c 0 1 ] ]) (betE a b c).