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Proof step 4 from proof ocs-put (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a = a0, m ≤ # x0, ∀ m, a. m < # x0 → x0[m] = a ∨ #oc(a, x0[m, a]) = #oc(a, x0) + 1 ∨ x0 = [] ⊦ (a0 ' + x0)[m] = a, #oc(a, (a0 ' + x0)[m, a]) = (#oc(a, a0 ') + #oc(a, x0)) + 1
Proof step 12:
m ≤ # x0, ∀ m, a. m < # x0 → x0[m] = a ∨ #oc(a, x0[m, a]) = #oc(a, x0) + 1 ∨ x0 = [] ⊦ a = a0, (a0 ' + x0)[m] = a, #oc(a, (a0 ' + x0)[m, a]) = (#oc(a, a0 ') + #oc(a, x0)) + 1

Rule argument

fma: a = a0

Additional information

Used formulas: a = a0