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

⊦ rmdup(x + mklist(a, n)) = rmdup(x) + a ', n = 0, a ∈ x

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, n. rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ n = 0 ∨ a ∈ x0 ⊦ rmdup((a0 + x0) + mklist(a, n)) = rmdup(a0 + x0) + a ', n = 0, a ∈ a0 + x0

Rule argument

indvar: x

Additional information

Used simplifier rules: mklist-rmdup-01: ⊦ n ≠ 0 → rmdup(mklist(a, n)) = a ';%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%rmdup-e: ⊦ rmdup([]) = []; from specification list-dup%c-04: ⊦ a ' = b ' ↔ a = b; from specification list