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 (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.
Let x16 of type ι be given.
Assume H2: x0 x3.
Assume H3: x0 x4.
Assume H4: x0 x5.
Assume H5: x0 x6.
Assume H6: x0 x7.
Assume H7: x0 x8.
Assume H8: x0 x9.
Assume H9: x0 x10.
Assume H10: x0 x11.
Assume H11: x0 x12.
Assume H12: x0 x13.
Assume H13: x0 x14.
Assume H14: x0 x15.
Assume H15: x0 x16.
Apply H1 with
x3,
x1 x4 (x1 x5 (x1 x6 (x1 x7 (x1 x8 (x1 x9 (x1 x10 (x1 x11 (x1 x12 (x1 x13 (x1 x14 x15)))))))))),
x16,
λ x17 x18 . x18 = x1 (x2 x3 x16) (x1 (x2 x4 x16) (x1 (x2 x5 x16) (x1 (x2 x6 x16) (x1 (x2 x7 x16) (x1 (x2 x8 x16) (x1 (x2 x9 x16) (x1 (x2 x10 x16) (x1 (x2 x11 x16) (x1 (x2 x12 x16) (x1 (x2 x13 x16) (x1 (x2 x14 x16) (x2 x15 x16)))))))))))) leaving 4 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_b6011236e1a22312171fb30ea3d87ed0b785ea60d02f5f2a289674442a86dda0 with
x0,
x1,
x4,
x5,
x6,
x7,
x8,
x9,
x10,
x11,
x12,
x13,
x14,
x15 leaving 13 subgoals.
The subproof is completed by applying H0.
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.
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.
The subproof is completed by applying H15.
set y17 to be ...
set y18 to be ...
Claim L16: ∀ x19 : ι → ο . x19 y18 ⟶ x19 y17
Let x19 of type ι → ο be given.
Assume H16: x19 (x3 (x4 x5 y18) (x3 (x4 x6 y18) (x3 (x4 x7 y18) (x3 (x4 x8 y18) (x3 (x4 x9 y18) (x3 (x4 x10 y18) (x3 (x4 x11 y18) (x3 (x4 x12 y18) (x3 (x4 x13 y18) (x3 (x4 x14 y18) (x3 (x4 x15 y18) (x3 (x4 x16 y18) (x4 y17 y18))))))))))))).
set y20 to be ...
Apply unknownprop_f54c0c06d6fb6a981c1e3de876e178a501ab3573d1d992c1ca1e32779dcfea1e with
x2,
x3,
x4,
x6,
x7,
x8,
x9,
x10,
x11,
x12,
x13,
x14,
x15,
x16,
y17,
y18,
λ x21 x22 . y20 (x3 (x4 x5 y18) ...) ... leaving 16 subgoals.
Let x19 of type ι → ι → ο be given.
Apply L16 with
λ x20 . x19 x20 y18 ⟶ x19 y18 x20.
Assume H17: x19 y18 y18.
The subproof is completed by applying H17.