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Proof step 12 from proof bag-add-rev (previous step)

⊦ count(n0, bag ++ n) = count(n0, bag ++ m ++ n), n0 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ count(n, bag0 ++ n0) = (n = n0 ⊃ 1;0) + count(n, bag0)
Proof step 14:
⊦ (n0 = n ⊃ 1;0) + count(n0, bag) = count(n0, bag ++ m ++ n), n0 = m

Rule argument

spec: bag-basic, inst: nat-bag name: count-insert seq: ⊦ count(n, bag0 ++ n0) = (n = n0 ⊃ 1;0) + count(n, bag0) subst: [n0, bag0, n] → [n, bag, n0] flags: <all paths>

Additional information

Used terms: n, bag, n0