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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιι be given.
Assume H0: ∀ x2 . x2x0∀ x3 . x3x0x1 x2 = x1 x3x2 = x3.
Let x2 of type ο be given.
Assume H1: ∀ x3 : ι → ι . inj x0 {x1 x4|x4 ∈ x0} x3x2.
Apply H1 with x1.
Apply andI with ∀ x3 . x3x0x1 x3{x1 x4|x4 ∈ x0}, ∀ x3 . x3x0∀ x4 . x4x0x1 x3 = x1 x4x3 = x4 leaving 2 subgoals.
The subproof is completed by applying ReplI with x0, x1.
The subproof is completed by applying H0.