Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Assume H1:
∀ x3 . In x3 x1 ⟶ ∃ x4 . and (In x4 x0) (x2 x4 = x3).
Apply unknownprop_12e58cc6d7fd37f7906c69ff3d21a270b69268795d2e712504eaf247a1053b07 with
λ x3 x4 : ι → ι → (ι → ι) → ο . x4 x0 x1 x2.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
inj x0 x1 x2,
∀ x3 . In x3 x1 ⟶ ∃ x4 . and (In x4 x0) (x2 x4 = x3) leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.