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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: SNo x1.
Assume H2: SNoLev x1 ∈ SNoLev x0.
Assume H3: SNoLt x1 x0.
Apply SepI with SNoS_ (SNoLev x0), λ x2 . SNoLt x2 x0, x1 leaving 2 subgoals.
Apply SNoS_I2 with x1, x0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
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