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.
Let x7 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.
Assume H7: x1 x7.
Let x8 of type ι be given.
Assume H8: x0 x8.
Apply unknownprop_0521dbe368717571f9f850eaad919a29f7906fa75f981f32010220d29ca2b6a8 with
x0,
x1,
x3,
x4,
x5,
x6,
x7,
x8,
λ x9 x10 . x2 x10 = x7 (x2 (x3 (x4 (x5 (x6 x8))))) leaving 9 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
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.
Apply unknownprop_ee7da36f82fa829b0612052894e469865a8742ba83804da207df2963b0cf406c with
x0,
x1,
x2,
x7,
x3,
x4,
x5,
x6,
x8 leaving 9 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H7.
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 H8.