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Theorem afs-cons-links-empty
⊦ afs-cons(dirs, files) → (links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0))
Type: A user defined theorem
Validity: The proof is valid.
Features: ws, lws,
Comment:
Used by:
afs-cons-links-rmorphans
,
afs-cons-nlink0-empty
,
orphans-del-dir
,
orphans-del-file
,
Used by units in proved state:
cache-asm
,
afs-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 10
Used lemmas:
afs-cons-notfile
,
afs-cons-file-nlink
,
afs-cons-dir-nlink
,
afs-cons-nlink0-notin
,
Used spec theorems:
Used simplifier rules:
abstract-file
/
elim
abstract-dir
/
elim
set-basic
/alink-set/
size-zero
set-basic
/alink-set/
size-zero-01