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Proof step 45 from proof rename-precond-abs (previous step)

fs[ri[inodekey(m3)]].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, fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → fs[ri[dentrykey(m3, str0)]].ino ≠ ROOT_INO ∧ abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, m3 = m4 → md = md0, ∀ 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), links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, 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)) = 0, links(m3, abs-dirs(fs, ri)) = ∅, m3 = ROOT_INO

User applied rule all left

And closed the goal!

Rule argument

pos: left 22 terms: m3 abort: F discard: F computed: T

Additional information

Used simplifier rules: ⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (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)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set] Used terms: m3