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Proof step 8 from proof rm-in-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
a ∈ x0, ∀ a. a ∈ x0 → a ∈ rmdup(x0) ⊦ a0 ∈ x0, a ∈ rmdup(x0)

Rule argument

Additional information

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