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Proof step 95 from proof rename-precond-abs (previous step)

fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink = 1, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, abs-dirs(fs, ri)[fs[ri[dentrykey(m3, str0)]].ino] = mkdir(m, md1, m0, m5, entries), 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 → 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)), fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, m3 = m4 → md = md0, ∀ name. dentrykey(fs[ri[dentrykey(m3, str0)]].ino, name) ∈ ri → inodekey(entries[name]) ∈ ri ∧ fs[ri[inodekey(entries[name])]].directory ∨ inodekey(entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(entries[name])]].directory, ∀ alink0. alink0 ∈ links(fs[ri[dentrykey(m3, str0)]].ino, abs-dirs(fs, ri)) ↔ alink0 ∈ ∅ ++ alink, 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, links(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m3, str0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink = 1, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, abs-dirs(fs, ri)[fs[ri[dentrykey(m3, str0)]].ino] = mkdir(m, md1, m0, m5, entries), 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) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → 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)), ∀ name. dentrykey(fs[ri[dentrykey(m3, str0)]].ino, name) ∈ ri → inodekey(entries[name]) ∈ ri ∧ fs[ri[inodekey(entries[name])]].directory ∨ inodekey(entries[name]) ∈ ri ∧ ¬ fs[ri[inodekey(entries[name])]].directory, ∀ alink0. inodekey(alink0.pino) ∈ ri ∧ fs[ri[inodekey(alink0.pino)]].directory ∧ dentrykey(alink0.pino, alink0.name) ∈ ri ∧ fs[ri[dentrykey(m3, str0)]].ino = fs[ri[dentrykey(alink0.pino, alink0.name)]].ino ↔ alink0 = alink, 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, links(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m3, str0)

Rule argument

Additional information

Used simplifier rules: ⊦ alink ∈ ∅ ++ alink0 ↔ alink = alink0; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name]; (s)