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Proof step 16 from proof refine-link (previous step)

fs[ri[inodekey(ino)]].nlink = 0, fs[ri[inodekey(ino)]].directory, 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), dentrykey(ino, str) ∈ ri, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(ino, str)]].ino) ∈ ri, inodekey(ino) ∈ ri, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(fs[ri[dentrykey(ino, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino, str)]].ino = ROOT_INO ⊦ # links(ino, abs-dirs(fs, ri)) = 0, ino = ROOT_INO, links(ino, abs-dirs(fs, ri)) = ∅, fs[ri[inodekey(fs[ri[dentrykey(ino, str)]].ino)]].directory, dentrykey(m, str0) ∈ ri, ∃ ino0. inodekey(ino0) ∈ ri ∧ (fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO) ∧ dentrykey(ino0, str) ∈ ri ∧ fs[ri[dentrykey(ino0, str)]].ino = fs[ri[dentrykey(ino, str)]].ino

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: valid-parent-ino-precond seq: ⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ∧ fs[ri[inodekey(m)]].directory ∧ inodekey(m) ∈ ri ∧ fo.inodes? ∧ ro.inodes? ∧ log-cons(log, fs) ∧ ri-inj(fi) ∧ ri-inj(ri) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ abs-keys(ro) = abs-keys(orphans(fs, ri)) ∧ (links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO) → valid-parent-ino(m, fs, ri, ro) subst: [fs, ri, m, fo, ro, log, fi] → [fs, ri, ino, fo, orphans(fs, ri), log, fi]

Additional information

Used simplifier rules: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → fo.inodes?; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ro.inodes?; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → log-cons(log, fs); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ri-inj(ri); (ss)%⊦ 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)%⊦ valid-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s) Used terms: fs, ri, ino, fo, orphans(fs, ri), log, fi