Let x0 of type ι → ο be given.
Let x1 of type (ι → ι) → ο be given.
Assume H0: ∀ x2 : ι → ι . x1 x2 ⟶ ∀ x3 . x0 x3 ⟶ x0 (x2 x3).
Assume H1: ∀ x2 x3 : ι → ι . x1 x2 ⟶ x1 x3 ⟶ ∀ x4 . x0 x4 ⟶ x2 (x3 x4) = x3 (x2 x4).
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ι be given.
Let x5 of type ι → ι be given.
Let x6 of type ι → ι be given.
Assume H2: x1 x2.
Assume H3: x1 x3.
Assume H4: x1 x4.
Assume H5: x1 x5.
Assume H6: x1 x6.
Let x7 of type ι be given.
Assume H7: x0 x7.
Apply H1 with
x2,
x3,
x4 (x5 (x6 x7)) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_726efda9cb61df3d507e02dc56ec2bf2c23da8346c61158565a39fe76654a6c4 with
x0,
x1,
x6,
x5,
x4,
x7 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H6.
The subproof is completed by applying H5.
The subproof is completed by applying H4.
The subproof is completed by applying H7.