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Proof step 16 from proof diff-add-sw (previous step)

count(a, bag1) = 0, count(a0, bag0 ++ a) < count(a0, bag1) ⊦ 0 = count(a0, (bag0 \ bag1) ++ a), count(a0, bag1) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ count(a, bag ++ b) = (a = b ⊃ 1;0) + count(a, bag)
Proof step 18:
count(a, bag1) = 0, (a0 = a ⊃ 1;0) + count(a0, bag0) < count(a0, bag1) ⊦ 0 = count(a0, (bag0 \ bag1) ++ a), count(a0, bag1) = 0

Rule argument

spec: bag-basic inst: name: count-insert seq: ⊦ count(a, bag ++ b) = (a = b ⊃ 1;0) + count(a, bag) subst: [b, bag, a] → [a, bag0, a0] flags: rewrite

Additional information

Used terms: a, bag0, a0