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Proof step 4 from proof ocs-put-01 (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: a = a0

Additional information

Used formulas: a = a0