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

m < # x ⊦ x[m] = a, #oc(a, x[m, a]) = #oc(a, x) + 1, x = []

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ m, a. m < # x0 → x0[m] = a ∨ #oc(a, x0[m, a]) = #oc(a, x0) + 1 ∨ x0 = [], m < #(a0 + x0) ⊦ (a0 + x0)[m] = a, #oc(a, (a0 + x0)[m, a]) = #oc(a, a0 + x0) + 1, a0 + x0 = []

Rule argument

indvar: x

Additional information

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