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Proof step 5 from proof rmdup-last (previous step)

a0 ∈ x0, ∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ 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 6:
a0 ∈ x0, ∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ rmdup(x0 + a ') = rmdup(x0) + a ', a ∈ x0

Rule argument

Additional information

Used simplifier rules: rm-in-05: ⊦ a ∈ x → rmdup(a ' + x + y) = rmdup(x + y);%rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);%a: ⊦ (x + y) + z = x + y + z; from specification list