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Theorem in-playload-data
n + m ≤ # zbrar ⊦ sorted(zbrar, 0, n + m) → (adr ∈ payload(zbrar, n, m) ↔ (∃ m0. n ≤ m0 ∧ m0 < n + m ∧ zbrar[m0].entry? ∧ zbrar[m0].adr = adr))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 20
Proof steps: 50
Used lemmas:
in-payload
,
payload-rec
,
payload-base
,
Used spec theorems:
store+set
/node-index/
Data-in
store+set
/node-index/
Data-in-other
Used simplifier rules:
nat-basic
/
add-base
store
/node-index/
In-empty
nat-basic
/
nls-fst
nat
/
ls-le-simp
nat-basic
/
l
zbranch-array-sorted
/
sorted-eq-entry-strong
nat-basic
/
eq-02
nat-basic
/
oz
zbranch
/
elim-03
nat-basic
/
succ
oelem
/nat-set/
transitivity
nat-basic
/
lf
nat-basic
/
l-01
nat
/
fle
nat-basic
/
f
nat
/
lels-03
nat-basic
/
l-02
nat
/
let
nat
/
fle-01
nat-basic
/
s-04
nat
/
succ-01
zbranch
/
inj-01
nat
/
le-ls-simp
zbranch
/
test-05
zbranch
/
sel-08
nat
/
lels
nat
/
anti
nat
/
ler
nat
/
lep
nat-basic
/
a
nat-basic
/
c