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Proof step 7 from proof diff (previous step)

∀ 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) ⊦ #oc(a, x \ y) ≤ #oc(a, x0 \ y0)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 8:
∀ 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, #oc(a, x \ y) ≤ #oc(a, x0 \ y0)

Rule argument

fma: a ∈ y

Additional information

Used simplifier rules: oc-diff: ⊦ a ∈ y → #oc(a, x \ y) = 0;% ⊦ 0 ≤ m; (s) Used formulas: a ∈ y