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Proof step 4 from proof rm-in-03 (previous step)

a ∈ a0 + x0, ∀ a. a ∈ x0 → a ∈ rmdup(x0) ⊦ a ∈ rmdup(a0 + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

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