| # links(entries0[str], dirs0) = m11 + 1, (ino = m0 ⊃ mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0) ;mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2) ) = mkdir(m19, md10, m20, m21, entries3), dirs0[ino] = mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), files0[entries0[str]] = mkfile(m5, md0, m11 + 1, content1), dirs0[m] = mkdir(m4, md6, # links(m, dirs0), m8, entries0), files0[ino] = mkfile(m12, md7, m13, content0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries0[str] ∈ files0, m0 ∈ dirs0, str ∈ entries0, entries1[str0] ∈ files0, str0 ∈ entries1, m ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = m, m = m0, m19 = # entries3, entries0[str] ∈ dirs0, entries1[str0] ∈ dirs0 |
Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ str ∈ entries → #(entries -- str) = (# entries)-1; (s)% ⊦ n -1 = n - 1; (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% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s) Used formulas: ino = m0