Let x0 of type ι → (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 → 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 → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4.
Apply unknownprop_7f8cf709626e3c3070e0159083b1ab8e788ca07cfe449c68d5a1358d4ee66821 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (e3162.. (f482f.. (e707a.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (e3162.. (f482f.. (e707a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (e707a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_49a26ed2e8c0e85eaecde06670270561b837d7f07fac28648201cb284750f907 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (e3162.. (f482f.. (e707a.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (e3162.. (f482f.. (e707a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
e3162.. (f482f.. (e707a.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
e3162.. (f482f.. (e707a.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
The subproof is completed by applying unknownprop_64706c046583f0aebfd798d86fb2bddc5986f4bf9579571a82843d1c7a79f3bb with x1, x2, x3, x4.
The subproof is completed by applying unknownprop_5fb65c286094f09917b7164094190b9100eedf8a4a5a58046fe9cc19dbc4a496 with x1, x2, x3, x4.