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Proof step 5 from proof subrec (previous step)

⊦ a ' + x ⊆m y ↔ a ∈ y ∧ (∀ a0. #oc(a0, x) ≤ #oc(a0, y -1l a))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y))
Proof step 7:
⊦ (∀ a0. #oc(a0, a ' + x) ≤ #oc(a0, y)) ↔ a ∈ y ∧ (∀ a0. #oc(a0, x) ≤ #oc(a0, y -1l a))

Rule argument

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

Additional information

Used terms: y, a ' + x