Let x0 of type ι → (ι → ο) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Assume H0:
∀ x3 : ι → ο . (∀ x4 . prim1 x4 x1 ⟶ iff (x2 x4) (x3 x4)) ⟶ x0 x1 x3 = x0 x1 x2.
Apply unknownprop_5ac7e58347fbd821fb6c06fd77c373ba625105663e23fa511d1e2827eb3c4615 with
x1,
x2,
λ x3 x4 . x0 x3 (decode_p (f482f.. (81bb1.. x1 x2) (4ae4a.. 4a7ef..))) = x0 x1 x2.
Apply H0 with
decode_p (f482f.. (81bb1.. x1 x2) (4ae4a.. 4a7ef..)).
Let x3 of type ι be given.
Apply unknownprop_12d3c711d3bd2930236f54800b174e3b630cb0c252b0ae281ac1e81b5d03da83 with
x1,
x2,
x3,
λ x4 x5 : ο . iff (x2 x3) x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x3.