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Theorem path-split

⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas: valid-dir-ino, path-rec, path-in-start, valid-ino, path-here,
Used spec theorems:
- Used simplifier rules:
  - list/path/Nil
  - list/path/a
  - list/path/c
  - abstract-dir/elim