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Proof step 4 from proof rm-notin-01 (previous step)

a ∈ rmdup(x), rmdup(x) = y + a ' + z ⊦ ¬ a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
rmdup(x) = y + a ' + z, a ∈ y, a ∈ x ⊦

Rule argument

Additional information

Used simplifier rules: rm-in-02: ⊦ a ∈ rmdup(x) ↔ a ∈ x;