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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x05.
Let x1 of type ιο be given.
Assume H1: x1 0.
Assume H2: x1 1.
Assume H3: x1 2.
Assume H4: x1 3.
Assume H5: x1 4.
Apply ordsuccE with 4, x0, x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H6: x04.
Apply cases_4 with x0, x1 leaving 5 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Assume H6: x0 = 4.
Apply H6 with λ x2 x3 . x1 x3.
The subproof is completed by applying H5.