[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem keys-mod
n < nused, m + nused ≤ # zbrar, zbrar[m + n].key = key, sorted(zbrar, m, nused) ⊦ keys(zbrar[m + n, mkzentry(key, adr)], m, nused) = keys(zbrar, m, nused) ++ key
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
keys-mod-0
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 13
Used lemmas:
keys-drop-lower
,
keys-rec
,
keys-base
,
Used spec theorems:
Used simplifier rules:
set-basic
/node-index/
ne
zbranch-array-sorted
/
sorted-base
nat-basic
/
zero-01
nat-basic
/
s-04
nat
/
lez
nat-basic
/
add-base
nat
/
fle
nat-basic
/
l-02
set-basic
/node-index/
add-01
zbranch
/
sel-04
array
/zbranch-array/
cgetput
nat
/
le-ls-simp
nat
/
lels
nat-basic
/
f
nat-basic
/
succ
array
/zbranch-array/
Size-put
array
/zbranch-array/
cngetput
nat-basic
/
oz
nat-basic
/
eq-02
nat-basic
/
a
nat-basic
/
c
zbranch-array-sorted
/
sorted-rec1
nat
/
succ-01
set-basic
/node-index/
eq-04