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Theorem difference
⊦ count(a, bag0 \ bag1) = (count(a, bag1) ≤ count(a, bag0) ⊃ count(a, bag0) - count(a, bag1);0)
Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by:
count-diff-subset
,
diff-add-sw
,
diff-swap
,
differente-notin
,
in-diff-notfirst
,
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: 7
Proof steps: 21
Used lemmas:
del-notin
,
count-del
,
diff-rec
,
diff-empty
,
Used spec theorems:
bag-basic
/
count-other
Used simplifier rules:
nat
/
lels
nat
/
anti
nat
/
zero
nat
/
lels-03
nat
/
sub-base
bag-basic
/
count-empty
nat-basic
/
zero
bag-basic
/
count-same
nat-basic
/
f
nat
/
ls
nat-basic
/
one-01
nat
/
le-def
nat-basic
/
oz
nat
/
cancel-01
nat-basic
/
a
nat-basic
/
c
nat
/
elim-pred-c
nat
/
le-one
nat
/
elim-sub
nat-basic
/
l-01
nat
/
leprf
nat
/
let
nat-basic
/
z-01