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Proof step 8 from proof rm-rm-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ y. rmdup(x0 + rmdup(y)) = rmdup(x0 + y) ⊦ rmdup(x0 + rmdup(y)) = rmdup(x0 + y), a ∈ x0, a ∈ rmdup(y), a ∈ y

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + y = x + z ↔ y = z; (s)% ⊦ a + x = a ' + x; (s)