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Proof step 11 from proof del (previous step)

a ∈ x, y ⊆m x -1l a ⊦ #oc(a, x) ≤ #oc(a, y) + 1 ∧ x -1l a ⊆m y ↔ x -1l a ⊆m y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
#oc(a, y) + 1 < #oc(a, x), a ∈ x, x -1l a ⊆m y, y ⊆m x -1l a ⊦

Rule argument

Additional information

Used simplifier rules: in-05: ⊦ a ∈ x → #oc(a, x) ≠ 0;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)