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Theorem path-one

⊦ ispath(str ', n, m, dirs, files) ↔ n ∈ dirs ∧ str ∈ dirs[n].entries ∧ (m ∈ dirs ∨ m ∈ files) ∧ dirs[n].entries[str] = m

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: expath-one, path-links-empty, path-split-one,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 3
Used lemmas: valid-ino, path-here, valid-dir-ino, path-rec,
Used spec theorems:
- Used simplifier rules:
  - abstract-dir/elim
  - list/path/app
  - list/path/a
  - abstract-dir/sel-09