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Proof step 3 from proof rm-size-01 (previous step)

a ∈ x ⊦ # rmdup(x + a ' + y) = # rmdup(x + y)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
a ∈ a0 + x0, ∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ # rmdup((a0 + x0) + a ' + y) = # rmdup((a0 + x0) + y)

Rule argument

term: x

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ ¬ a ∈ []; (s)