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Theorem keep-range
⊦ zbr.key = zbrar[m].key ∧ m < # zbrar ∧ n < nused ∧ nused ≤ # zbrar → key-range(zbrar[m, zbr], n, nused, ri) = key-range(zbrar, n, nused, ri)
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: 9
Proof steps: 21
Used lemmas:
range-last
,
range-one
,
range-first
,
range-inner
,
Used spec theorems:
array
/zbranch-array/
Put-other
Used simplifier rules:
nat-basic
/
succ
nat-basic
/
lf-02
nat-basic
/
zero
nat-basic
/
f
oelem
/nat-set/
irreflexivity
nat
/
succ-01
nat
/
lep-02
nat-basic
/
lf-01
nat
/
eqle-one
nat
/
les
nat
/
lels
nat
/
le-def
nat-basic
/
one-01
nat
/
ls-01
nat-basic
/
s-04
oelem
/nat-set/
ls-le
array
/zbranch-array/
Size-put
nat
/
elim-pred-c
nat-basic
/
oz
array
/zbranch-array/
ngp-10
array
/zbranch-array/
Put-same
nat-basic
/
eq-02
nat-basic
/
a
nat-basic
/
c
nat
/
fle