Let x0 of type ι → (ι → ι) → (ι → ο) → ι → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ο be given.
Let x4 of type ι be given.
Assume H0:
∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ 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_cd69b7539357c4811d4d3e9731775659c7e3a7ca880d8abea626c3c773516b37 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (f482f.. (f482f.. (1cd8e.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (1cd8e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (1cd8e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_830bd0c5517ce36e8642fbfe0630bd1ca102500c91c0d3fe2193586eb7194ac1 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (f482f.. (f482f.. (1cd8e.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (1cd8e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
f482f.. (f482f.. (1cd8e.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
decode_p (f482f.. (1cd8e.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_602da705b3bc36a02dadd202d3f84eb0c736cdcd4664d10955daea03c751c001 with x1, x2, x3, x4.
Let x5 of type ι be given.
Apply unknownprop_2f1aff5fbcba2a03771f3c198af9cd44ecc18862f1a3cef8c4d54a18aa638e5f 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.