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Proof step 14 from proof bag-add-rem-same (previous step)

∀ n. (∀ n0. count(n0, (bag0 -- n) ++ n) = count(n0, bag0)) ↔ count(n, bag0) ≠ 0 ⊦ (n = m ⊃ 1;0) + count(n, bag0) = 0, ∀ n0. count(n0, (m = n ⊃ bag0;(bag0 -- n) ++ m) ++ n) = count(n0, bag0 ++ m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
∀ n. (∀ n0. count(n0, (bag0 -- n) ++ n) = count(n0, bag0)) ↔ count(n, bag0) ≠ 0 ⊦ (n = m ⊃ 1;0) + count(n, bag0) = 0, count(n0, (m = n ⊃ bag0;(bag0 -- n) ++ m) ++ n) = count(n0, bag0 ++ m)

Proof step 14 from proof bag-add-rem-same (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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