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Proof step 4 from proof diff (previous step)

∀ a. #oc(a, y0) ≤ #oc(a, y), ∀ a. #oc(a, y) ≤ #oc(a, y0), ∀ a. #oc(a, x0) ≤ #oc(a, x), ∀ a. #oc(a, x) ≤ #oc(a, x0) ⊦ x \ y ⊆m x0 \ y0 ∧ x0 \ y0 ⊆m x \ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ a. #oc(a, y0) ≤ #oc(a, y), ∀ a. #oc(a, y) ≤ #oc(a, y0), ∀ a. #oc(a, x0) ≤ #oc(a, x), ∀ a. #oc(a, x) ≤ #oc(a, x0) ⊦ #oc(a, x \ y) ≤ #oc(a, x0 \ y0) ∧ #oc(a0, x0 \ y0) ≤ #oc(a0, x \ y)

Rule argument

Additional information

Used simplifier rules: msubset: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y));