Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι be given.
Assume H0:
x0 = d8d01.. x1 x2 x3 x4.
Let x5 of type ι → ο be given.
Assume H1:
∀ x6 . x5 x6 ⟶ prim1 x6 x1.
Apply H0 with
λ x6 x7 . x2 x5 = decode_c (f482f.. x7 (4ae4a.. 4a7ef..)) x5.
Apply unknownprop_a1109e80eebddd03ec86fb5e4a80ba8fed86666bac2429821c4ac4b346fe399a with
x1,
e0e40.. x1 x2,
d2155.. x1 x3,
x4,
λ x6 x7 . x2 x5 = decode_c x7 x5.
Let x6 of type ο → ο → ο be given.
Apply unknownprop_886a0247cbff495e94c1ec5112ed0f7c7f0106e52309f23fc3d66d990ba40bea with
x1,
x2,
x5,
λ x7 x8 : ο . x6 x8 x7.
The subproof is completed by applying H1.