Let x0 of type 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.
Assume H0:
∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ 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_493364ac88238c997501142687588779e16101987e5073e40eae76097712d5dd with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (f482f.. (f482f.. (5f184.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (5f184.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (5f184.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_40771ea886f80f98b32d1d881282250648392acc12c645469c87344f1af7fc17 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (f482f.. (f482f.. (5f184.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (5f184.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
f482f.. (f482f.. (5f184.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
f482f.. (f482f.. (5f184.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_28402dcc2ba78e14087bcd961f8274ab7fa38430ac7a3b1854b0846cad4bc690 with x1, x2, x3, x4.
The subproof is completed by applying unknownprop_82f0f89ba777ffd2c4f25e9fdd4a8b721fe1265d0911aa185e88a98c4ee67cc8 with x1, x2, x3, x4.