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Proof step 42 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, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), 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, 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, 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 insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ afs-cons(dirs, files) ↔ (∀ ino. ROOT_INO ∈ dirs ∧ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty(ino, dirs, files)) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino(dirs[ino].entries[name], dirs, files)) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → valid-pagesize(ino, n, files)))
Proof step 44:
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(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(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, m3 = m4 → md = md0, 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) = ∅, ∀ ino. ROOT_INO ∈ abs-dirs(fs, ri) ∧ (ino ∈ abs-dirs(fs, ri) ∧ ino ≠ ROOT_INO ∧ links(ino, abs-dirs(fs, ri)) = ∅ → dir-empty(ino, abs-dirs(fs, ri), abs-files(fs, ri))) ∧ ( ino ∈ abs-dirs(fs, ri) → ¬ ino ∈ abs-files(fs, ri) ∧ abs-dirs(fs, ri)[ino].nlink = # links(ino, abs-dirs(fs, ri)) ∧ abs-dirs(fs, ri)[ino].nlink ≤ 1 ∧ abs-dirs(fs, ri)[ino].size = # abs-dirs(fs, ri)[ino].entries ∧ abs-dirs(fs, ri)[ino].nsubdirs = # subdirs(ino, abs-dirs(fs, ri))) ∧ (ino ∈ abs-files(fs, ri) → ¬ ino ∈ abs-dirs(fs, ri) ∧ abs-files(fs, ri)[ino].nlink = # links(ino, abs-dirs(fs, ri))) ∧ (∀ name. ino ∈ abs-dirs(fs, ri) ∧ name ∈ abs-dirs(fs, ri)[ino].entries → valid-ino(abs-dirs(fs, ri)[ino].entries[name], abs-dirs(fs, ri), abs-files(fs, ri))) ∧ (∀ n. ino ∈ abs-files(fs, ri) ∧ n ∈ abs-files(fs, ri)[ino].content → valid-pagesize(ino, n, abs-files(fs, ri))), 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, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO ⊦ # links(m3, abs-dirs(fs, ri)) = 0, links(m3, abs-dirs(fs, ri)) = ∅, m3 = ROOT_INO

Rule argument

spec: afs-base name: afs-cons seq: ⊦ afs-cons(dirs, files) ↔ (∀ ino. ROOT_INO ∈ dirs ∧ ( ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty(ino, dirs, files)) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ ( ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino(dirs[ino].entries[name], dirs, files)) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → valid-pagesize(ino, n, files))) subst: [files, dirs] → [abs-files(fs, ri), abs-dirs(fs, ri)] flags: <all paths>

Additional information

Used terms: abs-files(fs, ri), abs-dirs(fs, ri)