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 → ι be given.
Let x4 of type ι → ο be given.
Assume H1:
∀ x5 . x4 x5 ⟶ prim1 x5 x1.
Apply H0 with
λ x5 x6 . x2 x4 = decode_c (f482f.. x6 (4ae4a.. 4a7ef..)) x4.
Apply unknownprop_d7d39a6ae9dd573b529ad4d558553a3d5dfa88cfa249f628a74ae5b338307a3e with
x1,
e0e40.. x1 x2,
eb53d.. x1 x3,
λ x5 x6 . x2 x4 = decode_c x6 x4.
Let x5 of type ο → ο → ο be given.
Apply unknownprop_886a0247cbff495e94c1ec5112ed0f7c7f0106e52309f23fc3d66d990ba40bea with
x1,
x2,
x4,
λ x6 x7 : ο . x5 x7 x6.
The subproof is completed by applying H1.