Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
λ x2 . struct_r (BinReln_product x2 x1).
Let x2 of type ι be given.
Let x3 of type ι → ι → ο be given.
Apply H1 with
λ x4 . struct_r (BinReln_product (pack_r x2 x3) x4).
Let x4 of type ι be given.
Let x5 of type ι → ι → ο be given.
Apply unknownprop_efcdca50692a8e5dea3b2dabd19b7c98b28ec0cd127c886a2f9539f6c2a2ba01 with
x2,
x3,
x4,
x5,
λ x6 x7 . struct_r x7.
The subproof is completed by applying pack_struct_r_I with
setprod x2 x4,
λ x6 x7 . and (x3 (ap x6 0) (ap x7 0)) (x5 (ap x6 1) (ap x7 1)).