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Proof step 7 from proof perm-all (previous step)

a ∈ x ∨ a ∈ y, ∀ a. #oc(a, x) ≤ #oc(a, y), #oc(a, y) ≤ #oc(a, x), ∀ a. #oc(a, y) ≤ #oc(a, x) ⊦ #oc(a, x) = #oc(a, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: oc-zero: ⊦ #oc(a, x) = 0 ↔ ¬ a ∈ x;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat