intros a b c d; try assumption.
apply transitive with (plus (plus (plus a b) c) d); auto.
apply transitive with (plus (plus (plus a c) b) d); auto.
apply compatible; auto.
apply transitive with (plus a (plus b c)); auto.
apply transitive with (plus a (plus c b)); auto.
apply compatible; auto.
Qed.

Theorem angle_inscrit :
forall A B M O : PO,
isocele O M A ->
isocele O M B ->
R (double (cons (vec M A) (vec M B))) (cons (vec O A) (vec O B)).