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Theorem union-write
m ≤ # asar, n < m ⊦ disj(asar, 0, m) → union(asar[n, as], 0, m) = (union(asar, 0, m) \ asar[n]) ∪ as
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 17
Used lemmas:
disj-rec
,
disj-union-rem
,
disj-in-both
,
in-union-ext
,
union-rec
,
union-base
,
union-write-above
,
Used spec theorems:
set-union
/address-list-set/
diff-union-03
set-union
/address-list-set/
empty-intersection-diff
set-basic
/address-list-set/
Extension
Used simplifier rules:
nat
/
fle
set-union
/address-list-set/
diff-e-01
nat-basic
/
zero-01
nat
/
lels
nat
/
ler
nat
/
anti
array
/address-set-array/
Put-same
set-union
/address-list-set/
une
set-union
/address-list-set/
diff-idem
set-basic
/address-list-set/
size-zero
set-basic
/address-list-set/
size-zero-01
set-basic
/address-list-set/
ne-01
set-union
/address-list-set/
int-c
set-union
/address-list-set/
int-a
set-union
/address-list-set/
Intersect
set-basic
/address-list-set/
In-empty
nat
/
lez
nat-basic
/
add-base
nat-basic
/
lf-02
nat-basic
/
lf-01
nat-basic
/
trans
nat-basic
/
succ
nat-basic
/
lf
nat-basic
/
f
nat-basic
/
ls-02
nat-basic
/
neq-01
nat
/
lels-02
nat-basic
/
neq-04
nat-basic
/
ref
nat-basic
/
s-04
nat
/
succ-01
array
/address-set-array/
Put-other
nat
/
lels-03
nat-basic
/
c
nat-basic
/
a
set-union
/address-list-set/
una
set-union
/address-list-set/
unc