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Proof step 12 from proof rm-rm-02 (previous step)

a ∈ rmdup(y), ∀ y. rmdup(x0 + rmdup(y)) = rmdup(x0 + y), a ∈ x0 ∨ a ∈ y ⊦ rmdup(x0 + rmdup(y)) = rmdup((a ' + x0) + y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: rm-in-02: ⊦ a ∈ rmdup(x) ↔ a ∈ x;%rm-in-04: ⊦ a ∈ y → rmdup(a ' + x + y) = rmdup(x + y);%a: ⊦ (x + y) + z = x + y + z; from specification list