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Proof step 7 from proof rmdup-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ a = a0, rmdup((a0 ' + x0) + a ') = (a0 ' + rmdup(x0)) + a ', a0 ∈ x0, a ∈ x0

Rule argument

Additional information

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