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Theorem difference

⊦ (bag0 \ bag1).count(a) = (bag1.count(a) ≤ bag0.count(a) ⊃ bag0.count(a) - bag1.count(a);0)

Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by: count-diff-subset, diff-add-sw, diff-swap, difference-notin, in-diff-notfirst, still-in-diff, union-diff-cancel, union-diff-distr,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 15
Used lemmas: count-del, del-notin, diff-rec, diff-empty,
Used spec theorems:
- bag-basic/count-other
Used simplifier rules: