Lemma l15_7_1 : 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.