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Proof step 3 from proof rmdup-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ rmdup((a0 ' + x0) + a ') = rmdup(a0 ' + x0) + a ', a = a0, a ∈ x0

Rule argument

Additional information

Used simplifier rules: in-06: ⊦ ¬ 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