| (ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) = mkdir(m15, md7, m16, m17, entries4), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), files[ino] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), dirs0[m0] = mkdir(m4, md5, # links(m0, dirs0), m7, entries0), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries2, entries2[str] ∈ dirs0, m0 ∈ dirs0, ROOT_INO ∈ dirs0, name ∈ entries4, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino = m0, m0 = m, entries4[name] ∈ files, entries4[name] ∈ dirs0, str0 ∈ entries0 |
Used simplifier rules: Del-at-entries: ⊦ (entries -- str0)[str] = (str ≠ str0 ⊃ entries[str];(∅)[str]);%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ str ∈ entries -- str0 ↔ str ≠ str0 ∧ str ∈ entries; (s)% ⊦ str ≠ str0 → (entries -- str0)[str] = entries[str]; (s)% ⊦ # ∅ = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: ino = m