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Proof step 3 from proof ocs-put-02 (previous step)

m ≤ # x0, ∀ m0, b0. x0[m0] ≠ b0 ∧ m0 < # x0 → #oc(x0[m0], x0[m0, b0]) = #oc(x0[m0], x0) - 1 ⊦ #oc((a0 ' + x0)[m], (a0 ' + x0)[m, b]) = #oc((a0 ' + x0)[m], a0 ') + #oc((a0 ' + x0)[m], x0) - 1, (a0 ' + x0)[m] = b

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
(a0 ' + x0)[m] = a0, m ≤ # x0, ∀ m0, b0. x0[m0] ≠ b0 ∧ m0 < # x0 → #oc(x0[m0], x0[m0, b0]) = #oc(x0[m0], x0) - 1 ⊦ #oc((a0 ' + x0)[m], (a0 ' + x0)[m, b]) = #oc((a0 ' + x0)[m], a0 ') + #oc((a0 ' + x0)[m], x0) - 1, (a0 ' + x0)[m] = b
Proof step 13:
m ≤ # x0, ∀ m0, b0. x0[m0] ≠ b0 ∧ m0 < # x0 → #oc(x0[m0], x0[m0, b0]) = #oc(x0[m0], x0) - 1 ⊦ (a0 ' + x0)[m] = a0, #oc((a0 ' + x0)[m], (a0 ' + x0)[m, b]) = #oc((a0 ' + x0)[m], a0 ') + #oc((a0 ' + x0)[m], x0) - 1, (a0 ' + x0)[m] = b

Rule argument

fma: (a0 ' + x0)[m] = a0

Additional information

Used formulas: (a0 ' + x0)[m] = a0