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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: In (SNoLev x1) (SNoLev x0).
Assume H1: SNoEq_ (SNoLev x1) x0 x1.
Assume H2: nIn (SNoLev x1) x0.
Apply unknownprop_7cfd5e4aadf2e8cb5956c30c3589cd3b6084bd1797b4cd3169e2a989d66e37fe with x0, x1.
Apply unknownprop_16a890d80e582f5663abfcfb5f5942164bae0e65476988fa667ed9ca882547fe with SNoLev x0, SNoLev x1, λ x2 . In x2 x0, λ x2 . In x2 x1 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_b7c7a090ca47d83894301167c54772cc587bbb21de668c0b72273825ec0064b9 with SNoLev x1, x0, x1.
The subproof is completed by applying H1.
Apply unknownprop_9bccc16873f624a3c3c071d170820d76e64a5491b15f0c2f0287b0026ecb19b8 with SNoLev x1, x0.
The subproof is completed by applying H2.