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Proof step 9 from proof bag-rem-empty (previous step)

bag -- n = ∅ ⊦ count(n1, bag) = count(n1, ∅ ++ n), count(n0, bag) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bag = bag2 ↔ (∀ n. count(n, bag) = count(n, bag2))
Proof step 11:
∀ n0. count(n0, bag -- n) = count(n0, ∅) ⊦ count(n0, bag) = 0, count(n1, bag) = count(n1, ∅ ++ n)

Rule argument

spec: bag-basic, inst: nat-bag name: extension seq: ⊦ bag = bag2 ↔ (∀ n. count(n, bag) = count(n, bag2)) subst: [bag2, bag] → [∅, bag -- n] flags: <all paths>

Additional information

Used terms: ∅, bag -- n