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Proof step 3 from proof ocs-put (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 4:
m < #(a0 + x0), ∀ m, a. m < # x0 → #oc(a, x0[m, a]) = #oc(a, x0) + 1 ∨ x0[m] = a ∨ x0 = [] ⊦ #oc(a, (a0 + x0)[m, a]) = #oc(a, a0 + x0) + 1, a0 + x0 = [], (a0 + x0)[m] = a

Rule argument

indvar: x

Additional information

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