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Theorem keys-inodekey-in
⊦ inodekey(n) ∈ ns.keys ↔ n ∈ ns
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
keys-in
,
keys-rec-full
,
keys-rem
,
Used by units in proved state:
gjournal-refine
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 9
Used lemmas:
keys-rec
,
keys-base
,
Used spec theorems:
set-basic
/nat-set/
Extension
set-basic
/nat-set/
indef
Used simplifier rules:
set-basic
/node-index/
In-empty
set-basic
/nat-set/
size-zero
set-basic
/nat-set/
size-zero-01
set-basic
/nat-set/
In-empty
nat-basic
/
oz
set-basic
/nat-set/
In-insert
key
/
inj-03
set-basic
/node-index/
In-insert
set-basic
/nat-set/
Size-insert
nat-basic
/
s-04
oelem
/nat-set/
irreflexivity
nat-basic
/
a
nat-basic
/
c