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Proof step 30 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 ⊦ is-open(ROOT_INO, of -- fd)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ is-open(ino, of) ↔ (∃ n. n ∈ of ∧ of[n].ino = ino)
Proof step 32:
files[ROOT_INO] = mkfile(m1, md, m2, content), of[fd] = mkfile(ROOT_INO, mode, m0), dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of ⊦ ∃ n. n ∈ of -- fd ∧ (of -- fd)[n].ino = ROOT_INO

Rule argument

spec: vfs-base name: is-open seq: ⊦ is-open(ino, of) ↔ (∃ n. n ∈ of ∧ of[n].ino = ino) subst: [of, ino] → [of -- fd, ROOT_INO] flags: <all paths>

Additional information

Used terms: of -- fd, ROOT_INO