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Proof step 4 from proof rm-in (previous step)

∀ a, y. a ∈ rmdup(x0 + y) ↔ a ∈ x0 ∨ a ∈ y ⊦ a ∈ rmdup((a0 + x0) + y) ↔ a ∈ a0 + x0 ∨ a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ a, y. a ∈ rmdup(x0 + y) ↔ a ∈ x0 ∨ a ∈ y ⊦ a ∈ rmdup((a0 ' + x0) + y) ↔ a ∈ a0 ' + x0 ∨ a ∈ y

Rule argument

Additional information

Used simplifier rules: ⊦ a + x = a ' + x; (s)