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_220466dabb9c90c9b087796465f1368ac3c1e9d1ef55643ebed4c27316fb8803 with
x4,
λ x5 x6 . If_i (09364.. x4 = f6917.. x6) (x2 x6) (x3 x6) = x3 x4.
Apply If_i_0 with
09364.. x4 = f6917.. x4,
x2 x4,
x3 x4.
Apply unknownprop_eb2fcd306f6f841b66fd8e32d0e8a446cfe3594d26b0bbf0192de86d9ef1a8f4 with
x4,
x4.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H0 with λ x6 x7 . x5 x7 x6.