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Proof step 33 from proof inv-close (previous step)

of[fd] = mkfile(ROOT_INO, mode, m0), files[ROOT_INO] = mkfile(m1, md, m2, content), dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ ∃ n. n ≠ fd ∧ n ∈ of ∧ of[n].ino = ROOT_INO

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files)
Proof step 35:
files[ROOT_INO] = mkfile(m1, md, m2, content), of[fd] = mkfile(ROOT_INO, mode, m0), dom of < ino0, afs-cons(dirs, files), fd ∈ of, ∀ n. n ∈ of → of[n].ino ∈ files ⊦ ∃ n. n ≠ fd ∧ n ∈ of ∧ of[n].ino = ROOT_INO

Rule argument

spec: vfs-base name: of-cons seq: ⊦ of-cons(of, dirs, files) ↔ (∀ n. n ∈ of → of[n].ino ∈ files) subst: [files, dirs, of] → [files, dirs, of] flags: <all paths>

Additional information

Used terms: files, dirs, of