Let x0 of type ι → (ι → ι → ο) → (ι → ο) → ι → ι 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.
Let x4 of type ι be given.
Assume H0:
∀ x5 : ι → ι → ο . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ iff (x2 x6 x7) (x5 x6 x7)) ⟶ ∀ x6 : ι → ο . (∀ x7 . prim1 x7 x1 ⟶ iff (x3 x7) (x6 x7)) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4.
Apply unknownprop_c9152796840c410a62ce994b0c774a129f2dd25c2fc66915b7cfb0ba0dbb18d5 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (2b2e3.. (f482f.. (e4ab3.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (e4ab3.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (e4ab3.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_bde2160fde0a8614929b4c96f813dfa1b3a6ed023b65cf1a27e4ace755a947cd with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (2b2e3.. (f482f.. (e4ab3.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (e4ab3.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
2b2e3.. (f482f.. (e4ab3.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
decode_p (f482f.. (e4ab3.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x5 of type ι be given.
Let x6 of type ι be given.
Apply unknownprop_205a8e50402a6e8cbed05df2f8d749d02992f9b6d93a4504b74ffeb148417bea with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x2 x5 x6) x7 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 x5 x6.
Let x5 of type ι be given.
Apply unknownprop_4e78cf47ffbdfabaacc771ac6807e8dd02581e54f1697892cd92679610639207 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.