Let x0 of type ι → (ι → ι → ι) → (ι → ο) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ο be given.
Assume H0:
∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3.
Apply unknownprop_9fa32bd638e8c31d6b182a5633791e799b87de2a4ba474c8268d6be18d528c69 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (e3162.. (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3.
Apply H0 with
e3162.. (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. 4a7ef..)),
decode_p (f482f.. (33a0d.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_4e0a023e0994003d0aeb1b6b3ffa0ab2be65253744ded6ca621dc0f96c465796 with x1, x2, x3.
Let x4 of type ι be given.
Apply unknownprop_fd2efe54fe67f3ab31cabede3eaf251effecfe7cd1887072248950b21a2f3196 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x3 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x3 x4.