[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 480 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]] = inodenode(key1, md2, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, links(m0, fs, ri) = ∅ ++ dentrykey(m, str), m ≠ 0, m0 ≠ ROOT_INO, m0 ≠ 0, m2 ≠ 0, m3 ≠ 0, fs[ri[inodekey(m0)]].directory, 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-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m0)] ∈ fs, ri[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ m2, 1 ≤ m3, ⌊err1⌋ , asynced → boolvar0, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, m1 ≠ 0 ∨ m = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ ((asynced → boolvar) ∧ err1 = err), ⟨let p_ino = m in {dirs := abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- str)]; dirs[p_ino].size := dirs[p_ino].size - 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs - 1; let ino = mkdentry(str, m0).ino in {files := abs-files(fs, ri); afs_drop_nlink#(ino; dirs, files)}; dent := negdentry(str); afs_inode_sync#(mkinode(m, md, true, m1, m2, m3); dirs, files); afs_inode_sync# (mkinode(m0, md0, true, 1, fs[ri[inodekey(dentrynode(key, m0).ino)]].nsubdirs, fs[ri[inodekey(dentrynode(key, m0).ino)]].size); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS}; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m1, m2, m3) = p_inode ∧ mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = c_inode ∧ mkdentry(str, m0) = dent ∧ err1 = err), m1 = 0 ∧ m ≠ ROOT_INO

User applied rule exists right

And obtained the following new goals

Proof step 481:
1 = fs[ri[inodekey(m0)]].nlink, fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), fs[ri[inodekey(m0)]] = inodenode(key1, md2, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, links(m0, fs, ri) = ∅ ++ dentrykey(m, str), fs[ri[inodekey(m0)]].directory, fo.inodes?, orphans(fs, ri).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-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m, str) ∈ ri, ri[dentrykey(m, str)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, 1 ≤ m3, 1 ≤ m2, ⌊err1⌋ , asynced → boolvar0, m1 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⌊err1⌋ ∧ ⟨err := err1; asynced := ?⟩ ((asynced → boolvar) ∧ err1 = err), ⟨let p_ino = m in {dirs := abs-dirs(fs, ri)[p_ino, abs-dirs(fs, ri)[p_ino].entries:= (abs-dirs(fs, ri)[p_ino].entries -- str)]; dirs[p_ino].size := dirs[p_ino].size - 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs - 1; let ino = mkdentry(str, m0).ino in {files := abs-files(fs, ri); afs_drop_nlink#(ino; dirs, files)}; dent := negdentry(str); afs_inode_sync#(mkinode(m, md, true, m1, m2, m3); dirs, files); afs_inode_sync# (mkinode(m0, md0, true, 1, fs[ri[inodekey(dentrynode(key, m0).ino)]].nsubdirs, fs[ri[inodekey(dentrynode(key, m0).ino)]].size); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS}; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m1, m2, m3) = p_inode ∧ mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = c_inode ∧ mkdentry(str, m0) = dent ∧ err1 = err), m = 0, m0 = ROOT_INO, m0 = 0, m2 = 0, m3 = 0, m1 = 0 ∧ m ≠ ROOT_INO

Rule argument

pos: right 1 terms: err1 abort: F discard: T computed: T

Additional information

Used terms: err1