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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ a. rmdup(x0 + a ') = rmdup(x0 -l a) + a ' ⊦ rmdup(x0 + a0 ') = rmdup(x0 -l a0) + a0 '

Rule argument

Additional information

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