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Proof step 32 from proof bag-add-rem-same (previous step)

∀ n. (∀ n0. count(n0, (bag0 -- n) ++ n) = count(n0, bag0)) ↔ count(n, bag0) ≠ 0 ⊦ count(n, bag0) = 0, count(n0, bag0 -- n) = count(n0, bag0), n = m, n0 = n, n0 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ m - 0 = m; (s) Used terms: n, bag0, n0