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Proof step 2 from proof rmdup-last (previous step)

⊦ rmdup(x + a ') = rmdup(x) + a ', a ∈ x

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ rmdup((a0 + x0) + a ') = rmdup(a0 + x0) + a ', a ∈ a0 + x0

Rule argument

term: x

Additional information

Used simplifier rules: rm-one: ⊦ rmdup(a ') = a ';%rmdup-e: ⊦ rmdup([]) = [];%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-04: ⊦ a ' = b ' ↔ a = b; from specification list