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Proof step 26 from proof inv-put-inode (previous step)

# links(of[n].ino, dirs) = 0, files[of[n].ino] = mkfile(m, md, 0, content), afs-cons(dirs, files -- of[n].ino), afs-cons(dirs, files), of-cons(of, dirs, files), of[n].ino ∈ files, n ∈ of ⊦ of[n].ino = ROOT_INO, is-open(of[n].ino, of), of[n].ino ∈ dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 27:
# links(m0, dirs) = 0, files[m0] = mkfile(m, md, 0, content), of[n] = mkfile(m0, mode, m1), afs-cons(dirs, files), afs-cons(dirs, files -- m0), of-cons(of, dirs, files), n ∈ of, m0 ∈ files ⊦ m0 = ROOT_INO, is-open(m0, of), m0 ∈ dirs

Rule argument

spec: file name: elim seq: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0) subst: [file, m, mode, m0] → [of[n], m0, mode, m1]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[n], m0, mode, m1