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Proof step 10 from proof rm-in-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);%in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list