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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 ιιι be given.
Assume H2: ∀ x4 . prim1 x4 x0∀ x5 . prim1 x5 x0prim1 (x3 x4 x5) x0.
Let x4 of type ιι be given.
Assume H3: ∀ x5 . prim1 x5 x0prim1 (x4 x5) x0.
Let x5 of type ιο be given.
Assume H4: ∀ x6 . ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x6∀ x9 . prim1 x9 x6prim1 (x7 x8 x9) x6)∀ x8 : ι → ι → ι . (∀ x9 . prim1 x9 x6∀ x10 . prim1 x10 x6prim1 (x8 x9 x10) x6)∀ x9 : ι → ι → ι . (∀ x10 . prim1 x10 x6∀ x11 . prim1 x11 x6prim1 (x9 x10 x11) x6)∀ x10 : ι → ι . (∀ x11 . prim1 x11 x6prim1 (x10 x11) x6)x5 (39199.. x6 x7 x8 x9 x10).
Apply H4 with x0, x1, x2, x3, x4 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.