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Theorem range-le
⊦ n + 1 < nused ∧ zbrar[n].key ≤ key ∧ nused ≤ # zbrar → key-range(zbrar, n, nused, ri |≤ key) = 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: 3
Proof steps: 9
Used lemmas:
range-first
,
range-inner
,
Used spec theorems:
node-index-restrict
/
restrict-norm
Used simplifier rules:
zbranch-array-sorted
/
le-key
nat-basic
/
one
nat-basic
/
succ
nat-basic
/
one-03
nat
/
succ-01
nat-basic
/
f
nat
/
elim-pred-c
nat
/
fle
nat-basic
/
c
nat-basic
/
a
nat-basic
/
oz
node-index-restrict
/
restrict-le3