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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.
Apply SNoEq_I with x1, binintersect x0 (SNoElts_ x1), x0.
Let x2 of type ι be given.
Assume H2: x2x1.
Apply iffI with x2binintersect x0 (SNoElts_ x1), x2x0 leaving 2 subgoals.
Assume H3: x2binintersect x0 (SNoElts_ x1).
Apply binintersectE1 with x0, SNoElts_ x1, x2.
The subproof is completed by applying H3.
Assume H3: x2x0.
Apply binintersectI with x0, SNoElts_ x1, x2 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply binunionI1 with x1, {SetAdjoin x3 (Sing 1)|x3 ∈ x1}, x2.
The subproof is completed by applying H2.