Let x0 of type ι → (ι → ι → ο) → (ι → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type 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 → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3.
Apply unknownprop_59ca09c0fd122f786673713c0642ed4ce1a31aabde53a2b0a8368edd8a739e79 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (2b2e3.. (f482f.. (42836.. x1 x2 x3) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (42836.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3.
Apply H0 with
2b2e3.. (f482f.. (42836.. x1 x2 x3) (4ae4a.. 4a7ef..)),
decode_p (f482f.. (42836.. 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_f9bb039047c575715dfc8b1b59b7b8ec67d811cbe7fb1bdb245069e08439d0a7 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.
Apply unknownprop_ccbf64b584877a997f6d8dee90614a29efc1b9f302b847ac9596ce2d25fc4cd2 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.