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Proof step 1 from proof subdel-03 (conclusion)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ x ⊆m y ↔ x -l a ⊆m y -l a ∧ #oc(a, x) ≤ #oc(a, y)
Proof step 3:
⊦ 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)

Rule argument

spec: inst: name: sub-del-any seq: ⊦ x ⊆m y ↔ x -l a ⊆m y -l a ∧ #oc(a, x) ≤ #oc(a, y) subst: [a, y, x] → [a, y -1l a, x] flags: rewrite, current

Additional information

Used terms: a, y -1l a, x