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Proof step 1 from proof possize-notin (conclusion)

⊦ pos(a, x) = # x ↔ ¬ a ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
pos(a, x) = # x, a ∈ x ⊦

Rule argument

Additional information

Used simplifier rules: notin-03: ⊦ ¬ a ∈ x → pos(a, x) = # x;