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Proof step 18 from proof unique-elems-add (previous step)

count(m, bag) = 0, ∀ n. count(n, bag) ≤ 1 ⊦ count(n, bag ++ m) = 0, count(n, bag ++ m) = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ count(n, bag0 ++ n0) = (n = n0 ⊃ 1;0) + count(n, bag0)
Proof step 20:
count(m, bag) = 0, ∀ n. count(n, bag) ≤ 1 ⊦ (n = m ⊃ 1;0) + count(n, bag) = 1, (n = m ⊃ 1;0) + count(n, bag) = 0

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] → [m, bag, n] flags: <all paths>

Additional information

Used terms: m, bag, n