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Proof step 3 from proof ocs-put-01 (previous step)

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: x

Additional information

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