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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ο be given.
Assume H0: ∀ x2 : ι → ι . inj 0 x0 x2x1.
Apply H0 with λ x2 . 0.
Apply andI with ∀ x2 . x200x0, ∀ x2 . x20∀ x3 . x300 = 0x2 = x3 leaving 2 subgoals.
Let x2 of type ι be given.
Assume H1: x20.
Apply FalseE with 0x0.
Apply EmptyE with x2.
The subproof is completed by applying H1.
Let x2 of type ι be given.
Assume H1: x20.
Apply FalseE with ∀ x3 . x300 = 0x2 = x3.
Apply EmptyE with x2.
The subproof is completed by applying H1.