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Proof step 6 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, a0 = a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ a, y. a ∈ rmdup(x0 + y) ↔ a ∈ x0 ∨ a ∈ y ⊦ a ∈ rmdup((a0 ' + x0) + y) ↔ a ∈ x0 ∨ a ∈ y, a0 = a

Rule argument

Additional information

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