Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Assume H0:
∀ x3 . In x3 x0 ⟶ In (x2 x3) x1.
Assume H1:
∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ x2 x3 = x2 x4 ⟶ x3 = x4.
Apply unknownprop_283f273b4f28592b1422a49659c7307e57b55f3b51858c4b8b39e82c747a5bc9 with
λ x3 x4 : ι → ι → (ι → ι) → ο . x4 x0 x1 x2.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
∀ x3 . In x3 x0 ⟶ In (x2 x3) x1,
∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ x2 x3 = x2 x4 ⟶ x3 = x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.