Proof step 519 from proof refine-rename-new-reparent (previous step)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

• Proof step 520:

  n0 + (boolvar1 ⊃ 1;0) = fs[ri[inodekey(m3)]].nsubdirs, m11 + 1 = fs[ri[inodekey(m3)]].size, boolvar ↔ false, boolvar0 ↔ false, dirs = dirs0[old_ino, dirs0[old_ino].size:= (dirs0[old_ino].size - 1)], dirs0 = abs-dirs(fs, ri) [old_ino, abs-dirs(fs, ri)[old_ino].entries:= (abs-dirs(fs, ri)[old_ino].entries -- mkdentry(str, fs[ri[dentrykey(m3, str)]].ino).name) ], new_ino = mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size).ino, old_dent = mkdentry(str, fs[ri[dentrykey(m3, str)]].ino), old_ino = mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, n0 + (boolvar1 ⊃ 1;0), m11 + 1).ino, fs[ri[dentrykey(m3, str)]].dentry?, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m7)]].directory, fs[ri[inodekey(m3)]].inode?, fs[ri[inodekey(m7)]].inode?, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m3) ∈ ri, inodekey(fs[ri[dentrykey(m3, str)]].ino) ∈ ri, inodekey(m7) ∈ ri, ri[inodekey(m3)] ∈ fs, ri[inodekey(m7)] ∈ fs, ri[dentrykey(m3, str)] ∈ fs, dentrykey(m3, str) ∈ ri, dirs0[old_ino].size ≥ 1, boolvar3 → boolvar4, ∀ adr, adr0, adr1, adr2. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs[ri[inodekey(m7)]].nlink ≠ 0 ∨ m7 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size, fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, fs[ri[inodekey(m7)]].trunc? ∨ fs[ri[inodekey(m7)]].inode? ⊦ ⟨if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1; dirs[new_ino].entries[str0] := old_dent.ino; new_dent := negdentry(str0); files := abs-files(fs, ri); if boolvar0 ∧ ¬ boolvar then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ boolvar0 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, n0 + (boolvar1 ⊃ 1;0), m11 + 1); dirs, files); afs_inode_sync#(mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size); dirs, files); new_child_inode := new_dent_inode; if boolvar0 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) )}; old_inode := getinode(mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, n0 + (boolvar1 ⊃ 1;0), m11 + 1).ino, dirs, files); new_inode := getinode(mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar2) ∧ mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, n0 + (boolvar1 ⊃ 1;0), m11 + 1) = old_inode ∧ mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size) = new_inode ∧ new_dent_inode = new_child_inode ∧ mkdentry(str, fs[ri[dentrykey(m3, str)]].ino) = old_dent ∧ negdentry(str0) = new_dent ∧ ENOSPC = err), ⟨err := ENOSPC; asynced := ?⟩ ((asynced → boolvar2) ∧ ENOSPC = err), m3 = m7, dentrykey(m7, str0) ∈ ri, fs[ri[inodekey(m7)]].nlink = 0 ∧ m7 ≠ ROOT_INO, fs[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdentry(str, m).name = str; (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 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