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Proof step 2 from proof diff-union (previous step)

⊦ ([] ∪ y) \ z = ([] \ z) ∪ (y \ z)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ rmdup(y) \ z = rmdup(y \ z)

Rule argument

Additional information

Used simplifier rules: empty-01: ⊦ [] ∪ x = rmdup(x);%assoc: ⊦ (x ∪ y) ∪ z = x ∪ y ∪ z;%diff-e: ⊦ [] \ y = [];