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Proof step 10 from proof rm-in-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
a ∈ rmdup(x0), ∀ a. a ∈ rmdup(x0) → a ∈ x0 ⊦ a = a0, a0 ∈ x0, a ∈ x0

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)