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.
Assume H2: x1 x2.
Assume H3: x1 x3.
Assume H4: x1 x4.
Let x5 of type ι be given.
Assume H5: x0 x5.
Apply H1 with
x3,
x4,
x5,
λ x6 x7 . x2 x7 = x4 (x2 (x3 x5)) leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Apply unknownprop_369fdf31a84537fcb40325ca4cd3b1e1dc3070515a73465cd8b13adde8b5da0f with
x0,
x1,
x2,
x4,
x3,
x5 leaving 6 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 H4.
The subproof is completed by applying H3.
The subproof is completed by applying H5.