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Proof step 14 from proof refine-unlink (previous step)

fs[ri[inodekey(m)]].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), inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, asynced → boolvar, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ∧ fs[ri[inodekey(m)]].directory ∧ inodekey(m) ∈ ri ∧ fo.inodes? ∧ orphans(fs, ri).inodes? ∧ log-cons(log, fs) ∧ ri-inj(fi) ∧ ri-inj(ri) ∧ replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log) ∧ ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log) ∧ abs-keys(orphans(fs, ri)) = abs-keys(orphans(fs, ri)) ∧ (links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO) → valid-parent-ino(m, fs, ri, orphans(fs, ri)), links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[dentrykey(m, str)]].ino ≠ ROOT_INO ∧ (fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO) ∧ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ≠ 0 ∧ (fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str)) ∧ 0 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ 1 ≤ fs[ri[inodekey(m)]].size

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
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), dentrykey(m, str) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, inodekey(m) ∈ ri, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[dentrykey(m, str)]].ino ≠ ROOT_INO ∧ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ≠ 0 ∧ (fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str)) ∧ 0 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ 1 ≤ fs[ri[inodekey(m)]].size

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)%⊦ valid-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, fs, ri, ro) ↔ ( valid-dir-ino(ino, fs, ri) ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO)) ∧ ¬ inodekey(ino) ∈ ro; (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ri-inj(ri); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → log-cons(log, fs); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ro.inodes?; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → fo.inodes?; (ss)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)