Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = 81bb1.. (f482f.. x1 4a7ef..) (decode_p (f482f.. x1 (4ae4a.. 4a7ef..))).
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Apply unknownprop_5ac7e58347fbd821fb6c06fd77c373ba625105663e23fa511d1e2827eb3c4615 with
x1,
x2,
λ x3 x4 . 81bb1.. x1 x2 = 81bb1.. x3 (decode_p (f482f.. (81bb1.. x1 x2) (4ae4a.. 4a7ef..))).
Apply unknownprop_b3166d21a658e1f65039669ebb2b483d998ce5411e8aafddea0483da5885c18a with
x1,
x2,
decode_p (f482f.. (81bb1.. x1 x2) (4ae4a.. 4a7ef..)).
Let x3 of type ι be given.
Apply unknownprop_12d3c711d3bd2930236f54800b174e3b630cb0c252b0ae281ac1e81b5d03da83 with
x1,
x2,
x3,
λ x4 x5 : ο . iff (x2 x3) x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x3.