Let x0 of type ι → (ι → ι) → (ι → ι) → ι → ι → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H0:
∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x2 x7 = x6 x7) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5.
Apply unknownprop_1a8f381c16116542cf8981afc4a588770c2be4163714f92d26507d232c5d0dfe with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x6 (f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x0 x1 x2 x3 x4 x5.
Apply unknownprop_c5e8a24eccb9b1e12261d8f9ffb66dafbcd6342a1cfe77f34a03a6e78aee65cb with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x1 (f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x0 x1 x2 x3 x4 x5.
Apply unknownprop_3f600adaa559a2f808a836946c4de597351b3b25462f406ca77a47eb3c503733 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x1 (f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) x4 x6 = x0 x1 x2 x3 x4 x5.
Apply H0 with
f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)),
f482f.. (f482f.. (264ee.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_30c66f46b94d71df93c58a823367f05e2a055abf6b4b846ea2584d471aed48c6 with x1, x2, x3, x4, x5.
The subproof is completed by applying unknownprop_1965786b645f22e2440b98e7d421332f5586f14d1905f3fab1d84dad0998c841 with x1, x2, x3, x4, x5.