Let x0 of type ι → ((ι → ο) → ο) → (ι → ι) → ι → ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Assume H0:
∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4.
Apply unknownprop_764acd696e647f6c1e13399f20c3d7a0c3012dbddcc1f8ac4bfc81ffd50a5120 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (decode_c (f482f.. (eb2d9.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (eb2d9.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (eb2d9.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_1524b180c69719302ec1be9fcae9d9a2668e7c2c94321e7b5052dbf5ecee2166 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (decode_c (f482f.. (eb2d9.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (eb2d9.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
decode_c (f482f.. (eb2d9.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
f482f.. (f482f.. (eb2d9.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x5 of type ι → ο be given.
Assume H1:
∀ x6 . x5 x6 ⟶ prim1 x6 x1.
Apply unknownprop_52bd681fb48f0194a26e56d7979f5439861b31be106e42108fdfa19b563fc551 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.
The subproof is completed by applying unknownprop_4712bc13b5160d975333d7566668b80deb133d8f8a6b96429e546b412c5a3772 with x1, x2, x3, x4.