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Proof step 10 from proof rmdup-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ 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: app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%in-17: ⊦ a ∈ b ' ↔ a = b; from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list