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.
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.
Apply unknownprop_f8cd2cc9fa3527ece23bf769ef6e4562a4db8193110bd03a6fde0a07ab4c38b8 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 x14)))))),
λ x15 x16 . x16 = x1 (x1 (x2 x3 x7) (x1 (x2 x3 x8) (x1 (x2 x3 x9) (x1 (x2 x3 x10) (x1 (x2 x3 x11) (x1 (x2 x3 x12) (x1 (x2 x3 x13) (x2 x3 x14)))))))) (x1 (x1 (x2 x4 x7) (x1 (x2 x4 x8) (x1 (x2 x4 x9) (x1 (x2 x4 x10) (x1 (x2 x4 x11) (x1 (x2 x4 x12) (x1 (x2 x4 x13) (x2 x4 x14)))))))) (x1 (x1 (x2 x5 x7) (x1 (x2 x5 x8) (x1 (x2 x5 x9) (x1 (x2 x5 x10) (x1 (x2 x5 x11) (x1 (x2 x5 x12) (x1 (x2 x5 x13) (x2 x5 x14)))))))) (x1 (x2 x6 x7) (x1 (x2 x6 x8) (x1 (x2 x6 x9) (x1 (x2 x6 x10) (x1 (x2 x6 x11) (x1 (x2 x6 x12) (x1 (x2 x6 x13) (x2 x6 x14)))))))))) leaving 8 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
Apply unknownprop_edbdc31c8b550a683544e2ad315a13cf7bd7f44068be39efa27faf89c5105937 with
x0,
x1,
x7,
x8,
x9,
x10,
x11,
x12,
x13,
x14 leaving 9 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.
The subproof is completed by applying H11.
The subproof is completed by applying H12.
The subproof is completed by applying H13.
The subproof is completed by applying H14.
Apply unknownprop_d0e822d4f75076294207423c07ba6080a94b4c48a2b85706a82f12d1ced35586 with
x0,
x1,
x2,
x7,
...,
...,
...,
...,
...,
...,
...,
...,
... leaving 12 subgoals.