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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 ιιι be given.
Assume H0: ∀ x3 . prim1 x3 x0∀ x4 . prim1 x4 x0x1 x3 x4 = x2 x3 x4.
Apply iffI with explicit_abelian x0 x1, explicit_abelian x0 x2 leaving 2 subgoals.
Apply explicit_abelian_repindep_imp with x0, x1, x2.
The subproof is completed by applying H0.
Apply explicit_abelian_repindep_imp with x0, x2, x1.
Let x3 of type ι be given.
Assume H1: prim1 x3 x0.
Let x4 of type ι be given.
Assume H2: prim1 x4 x0.
Let x5 of type ιιο be given.
Apply H0 with x3, x4, λ x6 x7 . x5 x7 x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.