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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιι be given.
Assume H0: ∀ x2 . prim1 x2 x0∀ x3 . prim1 x3 x0prim1 (x1 x2 x3) x0.
Let x2 of type ιιι be given.
Assume H1: ∀ x3 . prim1 x3 x0∀ x4 . prim1 x4 x0prim1 (x2 x3 x4) x0.
Let x3 of type ιο be given.
Assume H2: ∀ x4 . ∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x4∀ x7 . prim1 x7 x4prim1 (x5 x6 x7) x4)∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x4∀ x8 . prim1 x8 x4prim1 (x6 x7 x8) x4)x3 (b6bd3.. x4 x5 x6).
Apply H2 with x0, x1, x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.