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Proof step 13 from proof bag-add-rem-same (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: n abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ count(n, bag0 ++ n) = count(n, bag0) + 1; (s)% ⊦ n ≠ n0 → count(n, bag0 ++ n0) = count(n, bag0); (s)% ⊦ m = m + n ↔ n = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n