Let x0 of type ι → ο be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ι be given.
Assume H0: ∀ x3 x4 . x0 x3 ⟶ x0 x4 ⟶ x0 (x1 x3 x4).
Assume H1: ∀ x3 x4 x5 . x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x2 x3 (x1 x4 x5) = x1 (x2 x3 x4) (x2 x3 x5).
Assume H2: ∀ x3 x4 x5 . x0 x3 ⟶ x0 x4 ⟶ x0 x5 ⟶ x2 (x1 x3 x4) x5 = x1 (x2 x3 x5) (x2 x4 x5).
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Let x12 of type ι be given.
Let x13 of type ι be given.
Let x14 of type ι be given.
Let x15 of type ι be given.
Assume H3: x0 x3.
Assume H4: x0 x4.
Assume H5: x0 x5.
Assume H6: x0 x6.
Assume H7: x0 x7.
Assume H8: x0 x8.
Assume H9: x0 x9.
Assume H10: x0 x10.
Assume H11: x0 x11.
Assume H12: x0 x12.
Assume H13: x0 x13.
Assume H14: x0 x14.
Assume H15: x0 x15.
Apply unknownprop_bfc1cea51a42a4a32469869e8448699c1d59a9077d0b467664f278e66191db35 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15))))),
λ x16 x17 . x17 = x1 (x1 (x2 x3 x9) (x1 (x2 x3 x10) (x1 (x2 x3 x11) (x1 (x2 x3 x12) (x1 (x2 x3 x13) (x1 (x2 x3 x14) (x2 x3 x15))))))) (x1 (x1 (x2 x4 x9) (x1 (x2 x4 x10) (x1 (x2 x4 x11) (x1 (x2 x4 x12) (x1 (x2 x4 x13) (x1 (x2 x4 x14) (x2 x4 x15))))))) (x1 (x1 (x2 x5 x9) (x1 (x2 x5 x10) (x1 (x2 x5 x11) (x1 (x2 x5 x12) (x1 (x2 x5 x13) (x1 (x2 x5 x14) (x2 x5 x15))))))) (x1 (x1 (x2 x6 x9) (x1 (x2 x6 x10) (x1 (x2 x6 x11) (x1 (x2 x6 x12) (x1 (x2 x6 x13) (x1 (x2 x6 x14) (x2 x6 x15))))))) (x1 (x1 (x2 x7 x9) (x1 (x2 x7 x10) (x1 (x2 x7 x11) (x1 (x2 x7 x12) (x1 (x2 x7 x13) (x1 (x2 x7 x14) (x2 x7 x15))))))) (x1 ... ...))))) leaving 10 subgoals.