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Proof step 3 from proof delapp (previous step)

x = [] ⊦ (∀ a0. #oc(a0, x) + #oc(a0, y) ≤ #oc(a0, y -1l a)) ∧ (∀ a0. #oc(a0, y -1l a) ≤ #oc(a0, x) + #oc(a0, y)) ↔ x = [] ∧ ¬ a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ (∀ a0. #oc(a0, y) ≤ #oc(a0, y -1l a)) ∧ (∀ a0. #oc(a0, y -1l a) ≤ #oc(a0, y)) ↔ ¬ a ∈ y

Rule argument

Additional information

Used simplifier rules: oc-e: ⊦ #oc(a, []) = 0;%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%z: ⊦ 0 + m = m; from specification nat-basic2