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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Let x1 of type ι be given.
Assume H1: x1SNoLev x0.
Assume H2: x1x0.
Apply exactly1of2_E with x1x0, x1minus_SNo x0, nIn x1 (minus_SNo x0) leaving 3 subgoals.
Apply minus_SNo_exactly1of2 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H3: x1x0.
Assume H4: not (x1minus_SNo x0).
The subproof is completed by applying H4.
Assume H3: not (x1x0).
Apply FalseE with x1minus_SNo x0nIn x1 (minus_SNo x0).
Apply H3.
The subproof is completed by applying H2.