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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x01.
Let x1 of type ιο be given.
Assume H1: x1 0.
Apply ordsuccE with 0, x0, x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H2: x00.
Apply EmptyE with x0, x1 x0.
The subproof is completed by applying H2.
Assume H2: x0 = 0.
Apply H2 with λ x2 x3 . x1 x3.
The subproof is completed by applying H1.