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Proof step 4 from proof delapp (previous step)

⊦ (∀ a0. #oc(a0, y) ≤ #oc(a0, y -1l a)) ∧ (∀ a0. #oc(a0, y -1l a) ≤ #oc(a0, y)) ↔ ¬ a ∈ y

User applied rule case distinction

And obtained the following new goals

Proof step 5:
(∀ a0. #oc(a0, y) ≤ #oc(a0, y -1l a)) ∧ (∀ a0. #oc(a0, y -1l a) ≤ #oc(a0, y)) ⊦ ¬ a ∈ y

Rule argument

pos: right 1

Additional information

Used simplifier rules: in-02-01: ⊦ ¬ a ∈ x → x -1l a = x; from specification list-del%ler: ⊦ m ≤ m; from specification nat