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Theorem path-links-empty

⊦ ispath(p, ino, n, dirs, files) → (# links(n, dirs) = 0 ↔ p = ε ∧ links(ino, dirs) = ∅)

Type: A user defined theorem
Validity: The proof is valid.
Features: ws, lws,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 11
Used lemmas: links-nonempty, path-one, path-split, path-in-dirs, valid-ino, path-here,
Used spec theorems:
- list/path/lastdiv-rew
Used simplifier rules:
- set-basic/alink-set/size-zero
- set-basic/alink-set/size-zero-01
- set-basic/alink-set/Size-empty
- set-basic/alink-set/size-zero-02
- abstract-dir/elim