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Proof step 3 from proof subdel-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
x -l a ⊆m y -l a ⊦ #oc(a, x) ≤ #oc(a, y -1l a) ↔ #oc(a, x) < #oc(a, y) ∨ ¬ a ∈ x

Rule argument

Additional information

Used simplifier rules: del1-del: ⊦ (x -1l a) -l a = x -l a; from specification list-del