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Proof step 16 from proof ocs-put (previous step)

m ≤ # x0, ∀ m, a. m < # x0 → #oc(a, x0[m, a]) = #oc(a, x0) + 1 ∨ x0[m] = a ∨ x0 = [] ⊦ #oc(a, (a0 ' + x0)[m, a]) = 1 + #oc(a, x0), a0 ' + x0 = [], (a0 ' + x0).tail[m - 1] = a, a = a0, m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
m ≤ # x0, ∀ m, a. m < # x0 → #oc(a, x0[m, a]) = #oc(a, x0) + 1 ∨ x0[m] = a ∨ x0 = [] ⊦ #oc(a, (a0 ' + x0)[m, a]) = 1 + #oc(a, x0), x0[m - 1] = a, a = a0, m = 0

Rule argument

Additional information

Used simplifier rules: ⊦ a ' + x ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (a ' + x).tail = x; (s)