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Proof step 5 from proof bag-rem-subseteq (previous step)

count(n0, bag) < count(n0, bag -- n) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ count(n, bag0 -- n0) = count(n, bag0) - (n = n0 ∧ count(n, bag0) ≠ 0 ⊃ 1;0)
Proof step 7:
count(n0, bag) < count(n0, bag) - (n0 = n ∧ count(n0, bag) ≠ 0 ⊃ 1;0) ⊦

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, n0] flags: <all paths>

Additional information

Used terms: n, bag, n0