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Proof step 2 from proof ocs-put-01 (previous step)

m < # x ⊦ x[m] = a, a = b, #oc(a, x[m, b]) = #oc(a, x), x = []

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ m, a, b. m < # x0 → x0[m] = a ∨ a = b ∨ #oc(a, x0[m, b]) = #oc(a, x0) ∨ x0 = [], m < #(a0 + x0) ⊦ (a0 + x0)[m] = a, a = b, #oc(a, (a0 + x0)[m, b]) = #oc(a, a0 + x0), a0 + x0 = []

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;