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Theorem payload-mod
n < nused, m + nused ≤ # zbrar, zbrar[m + n].key = key, sorted(zbrar, m, nused) ⊦ payload(zbrar[m + n, mkzentry(key, adr)], m, nused) = payload(zbrar, m, nused)[key, adr]
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
payload-mod-0
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 25
Used lemmas:
payload-drop-lower
,
payload-rec
,
payload-base
,
Used spec theorems:
store
/node-index/
rew
zbranch-array-sorted
/
sorted-all
Used simplifier rules:
store
/node-index/
neq
zbranch-array-sorted
/
sorted-base
nat-basic
/
zero-01
nat
/
lez
nat
/
fle
nat-basic
/
l-02
zbranch
/
sel-08
array
/zbranch-array/
cgetput
nat
/
le-ls-simp
nat-basic
/
f
nat-basic
/
succ
array
/zbranch-array/
Size-put
array
/zbranch-array/
cngetput
nat-basic
/
eq-02
zbranch-array-sorted
/
sorted-rec1
zbranch
/
elim-03
zbranch
/
test-05
store
/node-index/
insins
nat
/
lels
nat
/
ls-le-simp
nat
/
succ-01
nat-basic
/
zero
nat-basic
/
oz
nat-basic
/
a
nat-basic
/
c
nat-basic
/
s-04
nat-basic
/
add-base
zbranch
/
sel-04
oelem
/key-order/
irreflexivity