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Proof step 1 from proof in-put (conclusion)

⊦ 1 < #oc(a, x) ∧ m < # x → a ∈ x[m, b]

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ a, m, b. 1 < #oc(a, x0) ∧ m < # x0 → a ∈ x0[m, b] ⊦ 1 < #oc(a, a0 + x0) ∧ m < #(a0 + x0) → a ∈ (a0 + x0)[m, b]

Rule argument

indvar: x

Additional information

Used simplifier rules: oc-e: ⊦ #oc(a, []) = 0;%list freely generated by [], +;;