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 unknownprop_26c80302b0a528fdb44581b0f4aaf59dc81bfaf868c43274bd7cba42973a25dc with
x0,
x1,
x3,
x4,
x5,
x6,
x7,
λ x8 x9 . x2 x9 = x6 (x2 (x3 (x4 (x5 x7)))) leaving 8 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.
Apply unknownprop_b8e8ce276b0a4954b7e17dd000c98a79a19bb4d9ffcc3cb7010552b09dee084c with
x0,
x1,
x2,
x6,
x3,
x4,
x5,
x7 leaving 8 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 H6.
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 H7.