intros A B C H; try assumption.
unfold double in |- *.
unfold isocele in H.
apply
transitive
with
(plus (cons (vec A C) (vec A B))
(plus (cons (opp (vec A B)) (vec B C))
(cons (opp (vec B C)) (opp (vec A C))))).
apply compatible.
apply reflexive.
apply compatible.
apply vR_R_compatible.
apply v_sym; apply opp_vect.
apply v_refl.
apply R_permute.
apply transitive with (cons (vec C A) (vec C B)).
try exact H.
apply vR_R_compatible.
apply v_sym; apply opp_vect.
apply v_sym; apply opp_vect.
apply somme_permute.
Qed.
Hint Resolve Chasles Chasles_2 angle_plat angle_nul oppu_u permute pi_plus_pi
u_oppv oppu_oppv oppu_v point_angle.plus_assoc plus_zero zero_plus_a
R_permute regulier plus_sym reflexive symetrique.

Lemma double_zero : R (double zero) zero.
unfold double in |- *.