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Proof step 121 from proof refine-unlink (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nlink, 0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, 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, false, 1, 0, m6), fs0[ri0[dentrykey(m, str)]].ino ≠ 0, fs0[ri0[dentrykey(m, str)]].ino ≠ ROOT_INO, fs0[ri0[inodekey(m)]].size ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, fs0[ri0[dentrykey(m, str)]].dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_unlink#(; 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, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1) = p_inode0 ∧ mkinode(fs0[ri0[dentrykey(m, str)]].ino, md0, false, 0, 0, m6) = p_inode1 ∧ negdentry(str) = old_dent ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 122:
fs0[ri0[inodekey(m)]].size = m0 + 1, 0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nlink, 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, false, 1, 0, m6), fs0[ri0[dentrykey(m, str)]].dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].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, fs0[ri0[inodekey(m)]].nsubdirs, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].size, asynced → boolvar0, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_unlink#(; 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, fs0[ri0[inodekey(m)]].nsubdirs, m0)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, m0)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, m0)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, m0)] [adr2, dentrynode(dentrykey(m, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6) ], (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, fs0[ri0[inodekey(m)]].nsubdirs, m0) = p_inode0 ∧ mkinode(fs0[ri0[dentrykey(m, str)]].ino, md0, false, 0, 0, m6) = p_inode1 ∧ negdentry(str) = old_dent ∧ ESUCCESS = err0), fs0[ri0[dentrykey(m, str)]].ino = 0, fs0[ri0[dentrykey(m, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [fs0[ri0[inodekey(m)]].size, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: fs0[ri0[inodekey(m)]].size, m0