Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Let x3 of type ι → ο be given.
Assume H2: x3 x0.
Apply unknownprop_b73af4382aa2130f443f8d39ac8ce95cd65e1e810ddcea4fbd727ebc17c2f4ca with
λ x4 x5 : ι → (ι → ο) → ι → (ι → ο) → ο . x5 x0 x2 x1 x3.
Apply unknownprop_55d33d10f6a09aaaea8e002117cf1820d9dc4418a57f04c18d4ec79694021a99 with
PNoLt_ (binintersect x0 x1) x2 x3,
and (and (In x0 x1) (PNoEq_ x0 x2 x3)) (x3 x0),
and (and (In x1 x0) (PNoEq_ x1 x2 x3)) (not (x2 x1)).
Apply unknownprop_c7bf67064987d41cefc55afb6af6ecbbb6b830405f2005e0def6e504b3ca3bf3 with
In x0 x1,
PNoEq_ x0 x2 x3,
x3 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.