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.
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.
Apply H2 with
x3,
x4,
x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))),
λ x11 x12 . x12 = x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x1 (x2 x3 x7) (x1 (x2 x3 x8) (x1 (x2 x3 x9) (x2 x3 x10)))))) (x1 (x2 x4 x5) (x1 (x2 x4 x6) (x1 (x2 x4 x7) (x1 (x2 x4 x8) (x1 (x2 x4 x9) (x2 x4 x10)))))) leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_14619fcdadc5a43502995316176da02be54150d716fe5c9727e811d162c28b04 with
x0,
x1,
x5,
x6,
x7,
x8,
x9,
x10 leaving 7 subgoals.
The subproof is completed by applying H0.
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.
The subproof is completed by applying H10.
Apply unknownprop_db57eabbae8f01f7ede64b544fc17e1b3344b7e5e868205273f289357efa3c25 with
x0,
x1,
x2,
x5,
x6,
x7,
x8,
x9,
x10,
x3,
λ x11 x12 . x1 x12 (x2 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 x10)))))) = x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x1 (x2 x3 x7) (x1 (x2 x3 x8) (x1 (x2 x3 x9) (x2 x3 x10)))))) (x1 (x2 x4 x5) (x1 (x2 x4 x6) (x1 (x2 x4 x7) (x1 (x2 x4 x8) (x1 (x2 x4 x9) (x2 x4 x10)))))) leaving 10 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
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.
The subproof is completed by applying H10.
The subproof is completed by applying H3.
Apply unknownprop_db57eabbae8f01f7ede64b544fc17e1b3344b7e5e868205273f289357efa3c25 with
x0,
x1,
x2,
x5,
x6,
x7,
x8,
x9,
x10,
x4,
λ x11 x12 . x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x1 (x2 x3 x7) (x1 (x2 x3 x8) (x1 (x2 x3 x9) (x2 x3 x10)))))) x12 = x1 ... ... leaving 10 subgoals.