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Proof step 4 from proof rm-in-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);%a: ⊦ (x + y) + z = x + y + z; from specification list