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Proof step 6 from proof ocs-put-01 (previous step)

a = a0, m ≤ # 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 ') + #oc(a, x0), (a0 ' + x0)[m] = a, a = b

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m ≤ # x0, ∀ m, a, b. m < # x0 → #oc(a, x0[m, b]) = #oc(a, x0) ∨ x0[m] = a ∨ a = b ∨ x0 = [] ⊦ #oc(a0, (a0 ' + x0)[m, b]) = 1 + #oc(a0, x0), (a0 ' + x0)[m] = a0, a0 = b

Rule argument

Additional information

Used simplifier rules: one: ⊦ #oc(a, a ') = 1;