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Proof step 4 from proof ocs-del-length (previous step)

∀ a, b. #oc(a, x0 -l b) = #oc(a, x0) ∨ a = b ⊦ a = b, #oc(a, (a0 ' + x0) -l 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, ∀ a, b. #oc(a, x0 -l b) = #oc(a, x0) ∨ a = b ⊦ a = b, #oc(a, (a0 ' + x0) -l b) = #oc(a, a0 ') + #oc(a, x0)
Proof step 7:
∀ a, b. #oc(a, x0 -l b) = #oc(a, x0) ∨ a = b ⊦ a = a0, a = b, #oc(a, (a0 ' + x0) -l b) = #oc(a, a0 ') + #oc(a, x0)

Rule argument

fma: a = a0

Additional information

Used formulas: a = a0