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Proof step 109 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, links(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m, str), ro = orphans(fs0, ri0), fs0[ri0[dentrykey(m, str)]].ino ≠ ROOT_INO, fs0[ri0[dentrykey(m, str)]].ino ≠ 0, fs0[ri0[inodekey(m)]].size ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, 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, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, asynced → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ [aubifs_core_orphans_insert# (inodekey(fs0[ri0[dentrykey(m, str)]].ino), (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3], fi, fo, 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) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ro); dent := negdentry(mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name); p_inode := mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).size); c_inode := mkinode (fs0[ri0[dentrykey(m, str)]].ino, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).meta, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).directory, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).nlink, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).nsubdirs, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).size)] ( 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], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ 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], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ 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]) ∧ 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], ro) ∧ ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]) ∧ 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) ]) ∧ ro.inodes? → ⟨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); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); 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(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ ESUCCESS = err0))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 110:
0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nsubdirs, 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].nlink, fs = 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) ], key = inodekey(fs0[ri0[dentrykey(m, str)]].ino), links(fs0[ri0[dentrykey(m, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3], ro = orphans(fs0, ri0), 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), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m, str)]].ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].size ≥ 1, asynced → boolvar0, fs0[ri0[inodekey(m)]].trunc? ∨ fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ [if key.inode? then ro := ro ++ key else abort; dent := negdentry(mkdentry(str, fs0[ri0[dentrykey(m, str)]].ino).name); p_inode := mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size - 1).size); c_inode := mkinode (fs0[ri0[dentrykey(m, str)]].ino, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).meta, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).directory, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).nlink, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).nsubdirs, inodenode(inodekey(fs0[ri0[dentrykey(m, str)]].ino), md0, false, 0, 0, m6).size)] ( 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], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ 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], ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ 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]) ∧ 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], ro) ∧ ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(fs0[ri0[dentrykey(m, str)]].ino), adr3]) ∧ 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) ]) ∧ ro.inodes? → ⟨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); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); 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(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ ESUCCESS = err0)), fs0[ri0[dentrykey(m, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m, str)]].ino = 0, fs0[ri0[inodekey(m)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_orphans_insert#(KEY, RI, FI, FO, FS, LOG, CSYNCED; RO) {if KEY.inode? then RO := RO ++ KEY else abort};