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Theorem range-put
n < nused, nused ≤ # zbrar, n ≠ 0 → zbrar[n - 1].key < key, nused ≠ 0 → key ≤ zbrar[n].key ⊦ key-range(zbrar, n, nused, ri[key, adr]) = key-range(zbrar, n, nused, ri)[key, 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: 10
Proof steps: 24
Used lemmas:
range-one
,
range-first
,
range-last
,
range-inner
,
at-range
,
Used spec theorems:
store
/node-index/
k-Extension
store
/node-index/
In-insert
store
/node-index/
At-other
node-index-restrict
/
at-le
Used simplifier rules:
zbranch-array-sorted
/
le-key
oelem
/nat-set/
irreflexivity
nat-basic
/
s-04
nat
/
lep-02
nat-basic
/
lf-01
nat
/
eqle-one
nat
/
les
nat
/
lels
nat
/
elim-pred-c
nat
/
succ-01
nat-basic
/
succ
nat-basic
/
lf-02
nat-basic
/
zero
nat-basic
/
f
store
/node-index/
In-insert
node-index-restrict
/
at-le
node-index-restrict
/
put-le
node-index-restrict
/
put-gt
nat
/
fle
nat-basic
/
c
nat-basic
/
a
nat-basic
/
oz
store
/node-index/
insin
store
/node-index/
At-same
store
/node-index/
At-other
node-index-restrict
/
in-le
store
/node-index/
in-neq
node-index-restrict
/
at-gt
node-index-restrict
/
in-gt