Let x0 of type ι → (ι → ι → ο) → (ι → ι → ο) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ι → ο be given.
Assume H0:
∀ x4 : ι → ι → ο . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ iff (x2 x5 x6) (x4 x5 x6)) ⟶ ∀ x5 : ι → ι → ο . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ iff (x3 x6 x7) (x5 x6 x7)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3.
Apply unknownprop_ba8500d70b6837e6ba201d4cb6447659635fe1e1465284d8fdf0e1c9742304e8 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3.
Apply H0 with
2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. 4a7ef..)),
2b2e3.. (f482f.. (08354.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_e73c46d626b1cba3a6b1ae73b9993b5fe8c340292b205804e43b4aa3b7e892f6 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x4 x5) x6 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x4 x5.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_a80b211237ab702683e3180bd24e2b20952c0f34a890418d470413fac50be678 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x3 x4 x5) x6 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x3 x4 x5.