[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 9 from proof orphans-del-file (previous step)

# links(ino, dirs) = 0, files[ino] = mkfile(n, md, 0, content), afs-cons(dirs, files), ino ∈ files ⊦ (ino0 ∈ dirs ∨ ino0 ≠ ino ∧ ino0 ∈ files) ∧ links(ino0, dirs) = ∅ ∧ ino0 ≠ ROOT_INO ↔ ino0 ≠ ino ∧ ino0 ∈ orphans(dirs, files), ino ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 11:
# links(ino, dirs) = 0, files[ino] = mkfile(n, md, 0, content), afs-cons(dirs, files), ino ∈ files ⊦ (ino0 ∈ dirs ∨ ino0 ≠ ino ∧ ino0 ∈ files) ∧ links(ino0, dirs) = ∅ ∧ ino0 ≠ ROOT_INO ↔ ino0 ≠ ino ∧ valid-ino(ino0, dirs, files) ∧ links(ino0, dirs) = ∅ ∧ ino0 ≠ ROOT_INO, ino ∈ dirs

Rule argument

spec: <toplevel> name: orphans seq: ⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO subst: [files, dirs, ino] → [files, dirs, ino0] flags: <all paths>

Additional information

Used terms: files, dirs, ino0