Lemma l15_7 : forall O E E' A B C H AB AC AH AC2, O<>E -> Per A C B -> Perp_at H C H A B -> Length O E E' A B AB -> Length O E E' A C AC -> Length O E E' A H AH -> (Prod O E E' AC AC AC2 <-> Prod O E E' AB AH AC2).