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Proof step 1 from proof bag-add2-eq-elim (conclusion)

⊦ bag0 ++ a ++ b ≠ bag1 ++ a ↔ bag0 ++ b ≠ 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:
⊦ ¬(∀ a0. count(a0, bag0 ++ a ++ b) = count(a0, bag1 ++ a)) ↔ bag0 ++ b ≠ bag1

Rule argument

spec: inst: name: extension seq: ⊦ bag0 = bag1 ↔ (∀ a. count(a, bag0) = count(a, bag1)) subst: [bag1, bag0] → [bag1 ++ a, bag0 ++ a ++ b] flags: rewrite, current

Additional information

Used terms: bag1 ++ a, bag0 ++ a ++ b