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Proof step 9 from proof diff (previous step)

#oc(a, x0 \ y0) < #oc(a, x), a ∈ x, ∀ a. #oc(a, x0) ≤ #oc(a, x), ∀ a. #oc(a, x) ≤ #oc(a, x0), ∀ a. #oc(a, y0) ≤ #oc(a, y), ∀ a. #oc(a, y) ≤ #oc(a, y0) ⊦ a ∈ y

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 10:
#oc(a, x0 \ y0) < #oc(a, x), a ∈ x, a ∈ y0, ∀ a. #oc(a, y) ≤ #oc(a, y0), ∀ a. #oc(a, y0) ≤ #oc(a, y), ∀ a. #oc(a, x) ≤ #oc(a, x0), ∀ a. #oc(a, x0) ≤ #oc(a, x) ⊦ a ∈ y
Proof step 12:
#oc(a, x0 \ y0) < #oc(a, x), a ∈ x, ∀ a. #oc(a, y) ≤ #oc(a, y0), ∀ a. #oc(a, y0) ≤ #oc(a, y), ∀ a. #oc(a, x) ≤ #oc(a, x0), ∀ a. #oc(a, x0) ≤ #oc(a, x) ⊦ a ∈ y, a ∈ y0

Rule argument

fma: a ∈ y0

Additional information

Used formulas: a ∈ y0