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Proof step 11 from proof rmdup-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ a = a0, rmdup(x0 + a ') = rmdup(x0) + a ', a0 ∈ x0, a ∈ x0

Rule argument

Additional information

Used simplifier rules: ⊦ x + y = x + z ↔ y = z; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)