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.
Assume H3: x0 x3.
Assume H4: x0 x4.
Assume H5: x0 x5.
Assume H6: x0 x6.
Assume H7: x0 x7.
Apply H2 with
x3,
x4,
x1 x5 (x1 x6 x7),
λ x8 x9 . x9 = x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x2 x3 x7))) (x1 (x2 x4 x5) (x1 (x2 x4 x6) (x2 x4 x7))) leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_a6006624829d7d44dfef146f097f47f429351018787d2b11ce9751df54eb1332 with
x0,
x1,
x5,
x6,
x7 leaving 4 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.
Apply unknownprop_647ec341c7696352fb8a30f001c79d84c2767a0fc283d06b71b39a980b6ecefe with
x0,
x1,
x2,
x5,
x6,
x7,
x3,
λ x8 x9 . x1 x9 (x2 x4 (x1 x5 (x1 x6 x7))) = x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x2 x3 x7))) (x1 (x2 x4 x5) (x1 (x2 x4 x6) (x2 x4 x7))) leaving 7 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 H3.
Apply unknownprop_647ec341c7696352fb8a30f001c79d84c2767a0fc283d06b71b39a980b6ecefe with
x0,
x1,
x2,
x5,
x6,
x7,
x4,
λ x8 x9 . x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x2 x3 x7))) x9 = x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x2 x3 x7))) (x1 (x2 x4 x5) (x1 (x2 x4 x6) (x2 x4 x7))) leaving 7 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 H4.
Let x8 of type ι → ι → ο be given.
Assume H8: x8 (x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x2 x3 x7))) (x1 (x2 x4 x5) (x1 (x2 x4 x6) (x2 x4 x7)))) (x1 (x1 (x2 x3 x5) (x1 (x2 x3 x6) (x2 x3 x7))) (x1 (x2 x4 x5) (x1 (x2 x4 x6) (x2 x4 x7)))).
The subproof is completed by applying H8.