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Lemma pythagoras_obtuse : forall O E E' A B C AC BC AB AC2 BC2 AB2 S2,
O<>E -> Obtuse A C B ->
Length O E E' A B AB -> Length O E E' A C AC -> Length O E E' B C BC ->
Prod O E E' AC AC AC2 -> Prod O E E' BC BC BC2 -> Prod O E E' AB AB AB2 ->
Sum  O E E' AC2 BC2 S2 -> LtP O E E' S2 AB2.