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Proof step 3 from proof sub-del-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y))
Proof step 5:
⊦ (∀ a. #oc(a, x) ≤ #oc(a, y)) ↔ (∀ a0. #oc(a0, x -l a) ≤ #oc(a0, y -l a)) ∧ #oc(a, x) ≤ #oc(a, y)

Rule argument

spec: inst: name: msubset seq: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y)) subst: [y, x] → [y -l a, x -l a] flags: rewrite, current

Additional information

Used terms: y -l a, x -l a