Let x0 of type ι → (ι → ι) → (ι → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ο be given.
Assume H0:
∀ x4 : ι → ι . (∀ x5 . prim1 x5 x1 ⟶ x2 x5 = x4 x5) ⟶ ∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3.
Apply unknownprop_d5c666295286bdabbe3b4b402072fcffded5f890a3391136bdff5cc6214a1e24 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (f482f.. (f482f.. (da24e.. x1 x2 x3) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (da24e.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3.
Apply H0 with
f482f.. (f482f.. (da24e.. x1 x2 x3) (4ae4a.. 4a7ef..)),
decode_p (f482f.. (da24e.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_4f3afbbe58bbb9a1658cfb089e3b5326b7bc654d1513ffdbae5a0e4dfeed0a85 with x1, x2, x3.
Let x4 of type ι be given.
Apply unknownprop_aa3a1ba9e3b66a6d45c93924e38055beb531cb5ca109751b2117af33661559ee 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.