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Proof step 6 from proof subset-antisym (previous step)

bag1 ⊆ bag0, bag0 ⊆ bag1 ⊦ count(a, bag0) = count(a, bag1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ bag0 ⊆ bag1 ↔ (∀ a. count(a, bag0) ≤ count(a, bag1))
Proof step 8:
bag0 ⊆ bag1, ∀ a. count(a, bag1) ≤ count(a, bag0) ⊦ count(a, bag0) = count(a, bag1)

Rule argument

spec: <toplevel> name: count-subset seq: ⊦ bag0 ⊆ bag1 ↔ (∀ a. count(a, bag0) ≤ count(a, bag1)) subst: [bag1, bag0] → [bag0, bag1] flags: <all paths>

Additional information

Used terms: bag0, bag1