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 → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Assume H0:
∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4.
Apply unknownprop_443af384f5a766563c87fe1d5f5df83d020f061721e547989a9faf36c7e3644e with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (e3162.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_b6909c5dff1fb43ebdc001458c5897fbb3ef3b47c78c20e1838eb8e968585acb with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (e3162.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (f482f.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
e3162.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
f482f.. (f482f.. (48567.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_e872f769d2f751d5ba4c285643abe39ba33ed9f3bd7608e4c63b386dc1f5861a with x1, x2, x3, x4.
The subproof is completed by applying unknownprop_aa5c741718ec84d60101c87f4b6d2bcc1b84ecd0ab92ad5cbef8a4e52fd8c3ad with x1, x2, x3, x4.