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Proof step 1 from proof subset-plusminus (conclusion)

⊦ count(a, bag1) ≠ 0 → (bag0 ⊆ bag1 -- a ↔ bag0 ++ a ⊆ bag1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ bag0 ⊆ bag1 ↔ (∀ a. count(a, bag0) ≤ count(a, bag1))
Proof step 3:
⊦ count(a, bag1) ≠ 0 → ((∀ a0. count(a0, bag0) ≤ count(a0, bag1 -- a)) ↔ bag0 ++ a ⊆ bag1)

Rule argument

spec: inst: name: count-subset seq: ⊦ bag0 ⊆ bag1 ↔ (∀ a. count(a, bag0) ≤ count(a, bag1)) subst: [bag1, bag0] → [bag1 -- a, bag0] flags: rewrite, current

Additional information

Used terms: bag1 -- a, bag0