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Theorem key-set-extract-index
n ≤ # kar ⊦ ki ∈ keyset(kar, n) ↔ (∃ m. m < n ∧ ki = kar[m])
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
key-index-in-keyset-array-extract
,
key-set-write-nodups
,
no-dups-idx-rec
,
no-dups-keyset-size
,
valid-idx-outofbounds
,
Used by units in proved state:
bin-min-heap-prepost
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 12
Used lemmas:
keyset-rec
,
keyset-base
,
Used spec theorems:
Used simplifier rules:
set-basic
/keyindex-set/
In-empty
nat-basic
/
zero-01
set-basic
/keyindex-set/
In-insert
nat
/
succ-01
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
nat
/
lels-03
nat-basic
/
ref
set-basic
/keyindex-set/
size-zero-01
nat-basic
/
succ
set-basic
/keyindex-set/
ne-01
nat-basic
/
trans
nat-basic
/
lf
nat-basic
/
f
nat-basic
/
ls-02
nat
/
fle-01
nat
/
lels
nat
/
anti