unfold eqo in H.
spliter.
unfold eq_o.
repeat split ; auto.
intros.
assert(HH:= H1 C C1 B2 M B' C' K).
apply HH; auto.
unfold proj in *.
spliter.
induction H13; induction H12.
spliter.
apply perp_in_per.
apply perp_in_comm.
apply perp_perp_in.
apply perp_sym.
Perp.
spliter.
apply perp_in_per.
apply perp_in_comm.
apply perp_perp_in.
apply perp_sym.
Perp.
spliter.
subst P.
apply l8_2.
apply l8_5.
spliter.
subst P.
apply l8_2.
apply l8_5.
unfold proj in *.
spliter.
induction H13; induction H12.
spliter.
apply perp_in_per.
apply perp_in_comm.
apply perp_perp_in.
apply perp_sym.
Perp.
spliter.
subst P1.
apply l8_2.
apply l8_5.
spliter.
apply perp_in_per.
apply perp_in_comm.
apply perp_perp_in.
apply perp_sym.
Perp.
spliter.
subst P1.
apply l8_2.
apply l8_5.
Qed.

Lemma eq_o_eqo : forall A B P A1 B1 P1, eq_o A B P A1 B1 P1 -> eqo A B P A1 B1 P1.
intros.