Let x0 of type ι be given.

Apply unknownprop_85336ee07ace71a942dc508d3b8c851d9d6bb88511443b7dafbf11b71c263f4d with λ x1 . ∃ x2 . aa8d2.. x1 x0 x2 leaving 2 subgoals.

Let x1 of type ο be given.

Assume H0: ∀ x2 . aa8d2.. 4a7ef.. x0 x2 ⟶ x1.

Apply H0 with x0.

The subproof is completed by applying unknownprop_f8eb3f19a7c6d972011b74d047027c2ca36c9a4aeb442692e92508e3371c0d54 with x0.

Let x1 of type ι be given.

Assume H0: ba9d8.. x1.

Assume H1: ∃ x2 . aa8d2.. x1 x0 x2.

Apply H1 with ∃ x2 . aa8d2.. (4ae4a.. x1) x0 x2.

Let x2 of type ι be given.

Assume H2: aa8d2.. x1 x0 x2.

Let x3 of type ο be given.

Assume H3: ∀ x4 . aa8d2.. (4ae4a.. x1) x0 x4 ⟶ x3.

Apply H3 with prim3 x2.

Apply unknownprop_a538fde2cb1c64ff6668f36b93c17f835ee2f07e6e0a0f90d30947fd8d72de1a with x0, x1, x2 leaving 2 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H2.

■

Proofgold Proof