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Proof step 36 from proof refine-rmdir (previous step)

fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs = # subdirs(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri)), fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size = 0, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[inodekey(ROOT_INO)]].directory, fo.inodes?, orphans(fs, ri).inodes?, 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-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m, str) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, inodekey(m) ∈ ri, inodekey(ROOT_INO) ∈ ri, asynced → boolvar, ∀ name. dentrykey(fs[ri[dentrykey(m, str)]].ino, name) ∈ ri → inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino)]].directory ∨ inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino)]].directory, ∀ 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), ∀ alink0. alink0 ∈ links(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri)) ↔ alink0 ∈ ∅ ++ alink, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ fs[ri[dentrykey(m, str)]].ino = ROOT_INO, links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs = # subdirs(fs[ri[dentrykey(m, str)]].ino, abs-dirs(fs, ri)), fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size = 0, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, fs[ri[inodekey(ROOT_INO)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[inodekey(m)]].directory, orphans(fs, ri).inodes?, fo.inodes?, 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-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(ROOT_INO) ∈ ri, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, asynced → boolvar, ∀ 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), ∀ name. dentrykey(fs[ri[dentrykey(m, str)]].ino, name) ∈ ri → inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino)]].directory ∨ inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(fs[ri[dentrykey(m, str)]].ino, name)]].ino)]].directory, ∀ alink0. inodekey(alink0.pino) ∈ ri ∧ fs[ri[inodekey(alink0.pino)]].directory ∧ dentrykey(alink0.pino, alink0.name) ∈ ri ∧ fs[ri[dentrykey(m, str)]].ino = fs[ri[dentrykey(alink0.pino, alink0.name)]].ino ↔ alink0 = alink, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ fs[ri[dentrykey(m, str)]].ino = ROOT_INO, links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str)

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)