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Proof step 133 from proof refine-rmdir (previous step)

fs0[ri0[inodekey(m)]].nsubdirs = m0 + 1, 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nlink, abs-children(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅, dentrykeys(inodekey(fs0[ri0[dentrykey(m, str)]].ino), ri0) = ∅, dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), links(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m, str), old_dent = mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino), p_inode0 = mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), p_inode1 = mkinode (fs0[ri0[dentrykey(m, str)]].ino, md0, true, 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size), fs0[ri0[dentrykey(m, str)]].dentry?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].inode?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3], orphans(fs0, ri0) ++ inodekey(fs0[ri0[dentrykey(m, str)]].ino)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3], orphans(fs0, ri0) ++ inodekey(fs0[ri0[dentrykey(m, str)]].ino), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3], orphans(fs0, ri0) ++ inodekey(fs0[ri0[dentrykey(m, str)]].ino), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].nsubdirs, 1 ≤ fs0[ri0[inodekey(m)]].size, asynced → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]) ∧ orphans (abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]), abs-files (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3])) = abs-keys(orphans(fs0, ri0)) ++ fs0[ri0[dentrykey(m, str)]].ino ∧ (asynced → boolvar) ∧ mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, m0, fs0[ri0[inodekey(m)]].size - 1) = p_inode0 ∧ mkinode (fs0[ri0[dentrykey(m, str)]].ino, md0, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].size) = p_inode1 ∧ negdentry(str) = old_dent ∧ ESUCCESS = err0), fs0[ri0[dentrykey(m, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m, str)]].ino = 0, fs0[ri0[inodekey(m)]].nsubdirs = 0, fs0[ri0[inodekey(m)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat