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Theorem sum-of-differences-rem
⊦ sum-of-differences(n, bag -- m) = (m ∈ bag ⊃ sum-of-differences(n, bag) - (n - m);sum-of-differences(n, bag))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
delta-write
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 11
Used lemmas:
sum-of-differences-in
,
sum-of-differences-rec
,
sum-of-differences-base
,
Used spec theorems:
Used simplifier rules:
bag-union
/nat-bag/
del-empty
bag-union
/nat-bag/
in-emp
bag-union
/nat-bag/
del-rec
bag-union
/nat-bag/
in-at
nat
/
eq-01
nat
/
ge
nat
/
add-01
bag-union
/nat-bag/
in-add
nat-basic
/
c
nat-basic
/
a
nat-basic
/
eq-01