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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x02.
Let x1 of type ιο be given.
Assume H1: x1 0.
Assume H2: x1 1.
Apply ordsuccE with 1, x0, x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H3: x01.
Apply cases_1 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H1.
Assume H3: x0 = 1.
Apply H3 with λ x2 x3 . x1 x3.
The subproof is completed by applying H2.