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Proof step 2 from proof rm-in-04 (previous step)

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

Heuristic structural induction applied rule structural induction

And obtained the following new goals

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

Rule argument

term: x

Additional information

Used simplifier rules: rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list