Proofgold Proof

pf
Let x0 of type ι be given. Assume H0: e581a.. x0. Apply dneg with ∃ x1 . prim1 x1 x0. Assume H1: not (∃ x1 . prim1 x1 x0). Apply H0. Let x1 of type ι be given. Assume H2: prim1 x1 x0. Apply H1. Let x2 of type ο be given. Assume H3: ∀ x3 . prim1 x3 x0 ⟶ x2. Apply H3 with x1. The subproof is completed by applying H2. ■