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.
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.
Apply unknownprop_b7b295f38ec44b7457473010f3621695d26e4e9422bae5a083cc6f30b9abc04b with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
x9,
x1 x10 (x1 x11 x12),
λ x13 x14 . x14 = x1 (x1 (x2 x3 x10) (x1 (x2 x3 x11) (x2 x3 x12))) (x1 (x1 (x2 x4 x10) (x1 (x2 x4 x11) (x2 x4 x12))) (x1 (x1 (x2 x5 x10) (x1 (x2 x5 x11) (x2 x5 x12))) (x1 (x1 (x2 x6 x10) (x1 (x2 x6 x11) (x2 x6 x12))) (x1 (x1 (x2 x7 x10) (x1 (x2 x7 x11) (x2 x7 x12))) (x1 (x1 (x2 x8 x10) (x1 (x2 x8 x11) (x2 x8 x12))) (x1 (x2 x9 x10) (x1 (x2 x9 x11) (x2 x9 x12)))))))) leaving 11 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.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
Apply unknownprop_a6006624829d7d44dfef146f097f47f429351018787d2b11ce9751df54eb1332 with
x0,
x1,
x10,
x11,
x12 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H10.
The subproof is completed by applying H11.
The subproof is completed by applying H12.
Apply unknownprop_647ec341c7696352fb8a30f001c79d84c2767a0fc283d06b71b39a980b6ecefe with
x0,
x1,
x2,
x10,
x11,
x12,
x3,
λ x13 x14 . x1 x14 (x1 (x2 x4 (x1 x10 (x1 x11 x12))) (x1 (x2 x5 (x1 x10 (x1 x11 x12))) (x1 (x2 x6 (x1 x10 (x1 x11 x12))) (x1 (x2 x7 (x1 x10 (x1 x11 x12))) (x1 (x2 x8 (x1 x10 (x1 x11 x12))) (x2 x9 (x1 x10 (x1 x11 x12)))))))) = x1 (x1 (x2 x3 x10) (x1 (x2 x3 x11) (x2 x3 ...))) ... leaving 7 subgoals.