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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: x1 ∈ SNoL x0.
Apply SNoL_E with x0, x1, x1 ∈ SNoS_ (SNoLev x0) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: SNo x1.
Assume H3: SNoLev x1 ∈ SNoLev x0.
Assume H4: SNoLt x1 x0.
Apply SNoS_I2 with x1, x0 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
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