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Proof step 1 from proof k-union-rec-n (conclusion)

⊦ ¬(a ∈ x ∨ a ∈ y) → (a + x) ∪ y = a + (x ∪ y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ rmdup((a ' + x) + y) = a ' + rmdup(x + y), a ∈ x, a ∈ y

Rule argument

Additional information

Used simplifier rules: union: ⊦ x ∪ y = rmdup(x + y);%assoc: ⊦ (x ∪ y) ∪ z = x ∪ y ∪ z;%c: ⊦ a + x = a ' + x; from specification list