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Proof step 5 from proof insert-inj (previous step)

bag0 ++ a = bag1 ++ a ⊦ count(a0, bag0) = count(a0, bag1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ bag0 = bag1 ↔ (∀ a. count(a, bag0) = count(a, bag1))
Proof step 7:
∀ a0. count(a0, bag0 ++ a) = count(a0, bag1 ++ a) ⊦ count(a0, bag0) = count(a0, bag1)

Rule argument

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

Additional information

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