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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιι be given.
Let x2 of type ι be given.
Assume H0: prim1 x2 x0.
Let x3 of type ι be given.
Assume H1: prim1 x3 x0.
Assume H2: ∀ x4 . prim1 x4 x0x1 x2 x4 = x4.
Assume H3: ∀ x4 . prim1 x4 x0x1 x4 x3 = x4.
Apply H3 with x2, λ x4 x5 . x4 = x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H2 with x3.
The subproof is completed by applying H1.