unfold Projp in H.
spliter.
induction H0.
spliter.
induction(eq_dec_points P' A).
subst P'.
right.
apply perp_not_eq_1 in H1.
assumption.
left.
assumption.
spliter.
subst P'.
induction(eq_dec_points P A).
subst P.
right.
assumption.
left.
assumption.
Qed.

Lemma projp_is_project_perp :
forall P P' A B,
Projp P P' A B ->
exists X, exists Y, Proj P P' A B X Y /\ Perp A B X Y.