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Proof step 14 from proof unique-elems-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ count(n, bag0 ++ n0) = (n = n0 ⊃ 1;0) + count(n, bag0)

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 simplifier rules: ⊦ m ≠ 0 → (m + n ≤ 1 ↔ m = 1 ∧ n = 0); (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m, bag, n