Let x0 of type ι → (ι → ο) → (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 → ο be given.
Let x4 of type ι be given.
Assume H0:
∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ο . (∀ x7 . prim1 x7 x1 ⟶ iff (x3 x7) (x6 x7)) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4.
Apply unknownprop_a576ff427cd318768867456a602be7385ebe63dbd963b27f10917adc75dc8282 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_192fd6bdb7e2fbd211637c744c2a289601fd6343dc99fbe58167f21d601083f0 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
decode_p (f482f.. (9a89f.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x5 of type ι be given.
Apply unknownprop_4548e98d35c6fb7e16df7a33511bfb2db06dacdf7d2ed47cd75df680654af064 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x5.
Let x5 of type ι be given.
Apply unknownprop_993bd80091dd1d96989c6f7e5192d0c5e7c03a63fa9eb1a1dcfc0ffe8d54833d with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x3 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x3 x5.