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Proof step 64 from proof refine-rmdir (previous step)

fs[ri[inodekey(m)]].nsubdirs = 0, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[inodekey(m)]].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-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, asynced → boolvar, ∀ str. str ∈ subdirs(m, abs-dirs(fs, ri)) ↔ str ∈ ∅, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ fs[ri[dentrykey(m, str)]].ino = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
fs[ri[inodekey(m)]].nsubdirs = 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, 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-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, asynced → boolvar, ∀ str0. ¬ dentrykey(m, str0) ∈ ri ∨ ¬ inodekey(fs[ri[dentrykey(m, str0)]].ino) ∈ ri ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ fs[ri[dentrykey(m, str)]].ino = ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ ∅; (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)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ str ∈ subdirs(ino, dirs) ↔ ino ∈ dirs ∧ str ∈ dirs[ino].entries ∧ dirs[ino].entries[str] ∈ dirs; (s)