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Proof step 7 from proof unique-elems-rem-notin (previous step)

unique-elems(bag) ⊦ count(m, bag -- n) = 0, m ≠ n ∧ m ∈ bag

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ count(n, bag0 -- n0) = count(n, bag0) - (n = n0 ∧ count(n, bag0) ≠ 0 ⊃ 1;0)
Proof step 9:
unique-elems(bag) ⊦ count(m, bag) - (m = n ∧ count(m, bag) ≠ 0 ⊃ 1;0) = 0, m ≠ n ∧ m ∈ bag

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, bag, m] flags: <all paths>

Additional information

Used terms: n, bag, m