[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 69 from proof rename-precond-abs (previous step)

fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink = 0, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(ROOT_INO)]].directory, orphans(fs, ri).inodes?, file-node-cons(fs, ri), log-cons(log, fs), 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), dentrykey(m3, str0) ∈ ri, inodekey(m4) ∈ ri, inodekey(m3) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri, inodekey(ROOT_INO) ∈ ri, m3 = m4 → md = md0, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, ∀ ino. (inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory ∧ ino ≠ ROOT_INO ∧ links(ino, abs-dirs(fs, ri)) = ∅ → abs-children(ino, fs, ri) = ∅) ∧ ( inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → fs[ri[inodekey(ino)]].nlink = # links(ino, abs-dirs(fs, ri)) ∧ fs[ri[inodekey(ino)]].nlink ≤ 1 ∧ fs[ri[inodekey(ino)]].size = # abs-children(ino, fs, ri) ∧ fs[ri[inodekey(ino)]].nsubdirs = # subdirs(ino, abs-dirs(fs, ri))) ∧ (inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → fs[ri[inodekey(ino)]].nlink = # links(ino, abs-dirs(fs, ri))) ∧ (∀ name. inodekey(ino) ∈ ri ∧ dentrykey(ino, name) ∈ ri → inodekey(abs-dirs(fs, ri)[ino].entries[name]) ∈ ri ∧ fs[ri[inodekey(abs-dirs(fs, ri)[ino].entries[name])]].directory ∨ inodekey(abs-dirs(fs, ri)[ino].entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(abs-dirs(fs, ri)[ino].entries[name])]].directory), fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∧ boolvar ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m1 = 0 ∧ ¬ boolvar, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ boolvar0 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m7 = 0 ∧ ¬ boolvar0, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO ⊦ fs[ri[dentrykey(m3, str0)]].ino = ROOT_INO

User applied rule all left

And obtained the following new goals

Proof step 70:
fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink = 0, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, fs[ri[inodekey(ROOT_INO)]].directory, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m3)]].directory, orphans(fs, ri).inodes?, file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(ROOT_INO) ∈ ri, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m3, str0) ∈ ri, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, m3 = m4 → md = md0, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ fs[ri[dentrykey(m3, str0)]].ino ≠ ROOT_INO ∧ links(fs[ri[dentrykey(m3, str0)]].ino, abs-dirs(fs, ri)) = ∅ → abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink = # links(fs[ri[dentrykey(m3, str0)]].ino, abs-dirs(fs, ri)) ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ≤ 1 ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size = # abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs = # subdirs(fs[ri[dentrykey(m3, str0)]].ino, abs-dirs(fs, ri)), inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink = # links(fs[ri[dentrykey(m3, str0)]].ino, abs-dirs(fs, ri)), ∀ name. inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ dentrykey(fs[ri[dentrykey(m3, str0)]].ino, name) ∈ ri → inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m3, str0)]].ino].entries[name]) ∈ ri ∧ fs[ri[inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m3, str0)]].ino].entries[name])]].directory ∨ inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m3, str0)]].ino].entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(abs-dirs(fs, ri)[fs[ri[dentrykey(m3, str0)]].ino].entries[name])]].directory, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ boolvar0 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m7 = 0 ∧ ¬ boolvar0, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∧ boolvar ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m1 = 0 ∧ ¬ boolvar ⊦ fs[ri[dentrykey(m3, str0)]].ino = ROOT_INO

Rule argument

pos: left 22 terms: fs[ri[dentrykey(m3, str0)]].ino abort: F discard: T computed: T

Additional information

Used terms: fs[ri[dentrykey(m3, str0)]].ino