Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Apply unknownprop_31dc82295b7aa4a340f2278c1cf4aa729add061fe389e3a99b659752ce7d8635 with
x4,
λ x5 x6 . If_i (f6917.. x4 = f6917.. x6) (x2 x6) (x3 x6) = x2 x4.
Apply If_i_1 with
f6917.. x4 = f6917.. x4,
x2 x4,
x3 x4.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H0.