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Proof step 4 from proof subdel (previous step)

x ⊆m y -1l a ⊦ ∀ a. #oc(a, x) ≤ #oc(a, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
#oc(a0, y) < #oc(a0, x), x ⊆m y -1l a, a0 ∈ x ⊦

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-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat