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Proof step 12 from proof rmdup-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
∀ a. rmdup(x0 + a ') = rmdup(x0 -l a) + a ' ⊦ a = a0, (a0 ∈ x0 ⊃ rmdup(x0 + a ');a0 ' + rmdup(x0 + a ')) = rmdup(a0 ' + (x0 -l a)) + a '

Rule argument

Additional information

Used simplifier rules: 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