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Theorem afs-cons-nlink0-notin

⊦ afs-cons(dirs, files) ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files → links(ino, dirs) = ∅

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: afs-cons-links-empty,
Used by units in proved state: cache-asm, afs-contracts, afs-asm,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 7
Used lemmas: afs-cons-in-next, links-nonempty, links,
Used spec theorems:
- set-basic/alink-set/Extension
Used simplifier rules:
- set-basic/alink-set/In-empty
- alink/elim
- set-basic/alink-set/size-zero-01
- set-basic/alink-set/size-zero
- abstract-dir/elim