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Proof step 1 from proof oc-del (conclusion)

⊦ ¬ #oc(a, x) < #oc(a, x -1l b)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
#oc(a, x) < #oc(a, x -1l b), a ∈ x -1l b, a ∈ x ⊦

Rule argument

Additional information

Used simplifier rules: oc-zero: ⊦ #oc(a, x) = 0 ↔ ¬ a ∈ x;%in-01-01: ⊦ a ∈ x -1l b → a ∈ x; (forward) from specification list-del%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1