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Proof step 2 from proof k-union-rec-n (previous step)

⊦ (a + x) ∪ y = a + (x ∪ y), a ∈ x, a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ rmdup((a ' + x) + y) = a ' + rmdup(x + y), a ∈ y, a ∈ x

Rule argument

Additional information

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