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Proof step 8 from proof ocs-same-length-mklist (previous step)

∀ a. #oc(a, x0) = # x0 ↔ x0 = mklist(a, # x0) ⊦ #oc(a, a0 ') + #oc(a, x0) = # x0 + 1 ↔ a0 = a ∧ x0 = mklist(a, # x0)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 9:
a = a0, ∀ a. #oc(a, x0) = # x0 ↔ x0 = mklist(a, # x0) ⊦ #oc(a, a0 ') + #oc(a, x0) = # x0 + 1 ↔ a0 = a ∧ x0 = mklist(a, # x0)
Proof step 11:
∀ a. #oc(a, x0) = # x0 ↔ x0 = mklist(a, # x0) ⊦ a = a0, #oc(a, a0 ') + #oc(a, x0) = # x0 + 1 ↔ a0 = a ∧ x0 = mklist(a, # x0)

Rule argument

fma: a = a0

Additional information

Used formulas: a = a0