Let x0 of type ι → (ι → ο) → ι → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Let x3 of type ι be given.
Assume H0:
∀ x4 : ι → ο . (∀ x5 . prim1 x5 x1 ⟶ iff (x2 x5) (x4 x5)) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3.
Apply unknownprop_a24d00d7d58489d5e03d60c0e95229905bfc68c6753101dbb87b43d46b7bffe2 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (decode_p (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) = x0 x1 x2 x3.
Apply unknownprop_e800aee987e9a3dc43bc88979595ea06431689cd684eb2e3aa9b1f10aef3d05c with
x1,
x2,
x3,
λ x4 x5 . x0 x1 (decode_p (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4 = x0 x1 x2 x3.
Apply H0 with
decode_p (f482f.. (5f5a0.. x1 x2 x3) (4ae4a.. 4a7ef..)).
Let x4 of type ι be given.
Apply unknownprop_40730fb0a004b91a28776735d67465e69576d851dd9fd3b6f48aaa88954c688b with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x4.