proposition: Lemma lcos3_permut1 : forall lp l a b c, Lcos3 lp l a b c -> Lcos3 lp l a c b.
proof: Proof. intros. assert(HH:= lcos3_lcos_1_2 lp l a b c). destruct HH. assert(exists la : Tpoint -> Tpoint -> Prop, Lcos la l a /\ Lcos2 lp la b c). apply lcos3_lcos_1_2; auto. ex_and H2 la. apply lcos2_comm in H3. apply lcos3_lcos_1_2. exists la. split; auto. Qed.
imports: GeoCoq.Tarski_dev.Ch13_3_angles Morphisms