unfold EqV in H.
induction H.
apply plg_cong.
apply plg_permut.
apply plg_comm2.
assumption.
spliter.
subst B.
subst D.
Cong.
Qed.

Lemma project_preserves_eqv :
forall P Q R S P' Q' R' S' A B X Y, EqV P Q R S ->
Proj P P' A B X Y ->
Proj Q Q' A B X Y ->
Proj R R' A B X Y ->
Proj S S' A B X Y ->
EqV P' Q' R' S'.