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Proof step 2 from proof notin (previous step)

⊦ a ' ∪ x = a ' + rmdup(x), a ∈ x

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: union: ⊦ x ∪ y = rmdup(x + y);%assoc: ⊦ (x ∪ y) ∪ z = x ∪ y ∪ z;% ⊦ x + y = x + z ↔ y = z; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)% ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); (s)