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Proof step 334 from proof refine-link (previous step)

fs[ri[dentrykey(ino1, str)]].ino = fs[ri[dentrykey(ino2, str)]].ino, 0 = fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nsubdirs, fs[ri[dentrykey(ino0, str)]] = dentrynode(key, fs[ri[dentrykey(ino2, str)]].ino), dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), old_dent0 = negdentry(str0), p_inode0 = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode1 = mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink, 0, m6), fs[ri[dentrykey(ino2, str)]].ino ≠ 0, m ≠ 0, fs[ri[inodekey(ino0)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(ino2)]].directory, fs[ri[inodekey(m)]].inode?, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].inode?, 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-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(ino2) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(fs[ri[dentrykey(ino2, str)]].ino) ∈ ri, ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)] ∈ fs, inodekey(ino0) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(ino1) ∈ ri, dentrykey(ino2, str) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, dentrykey(ino0, str) ∈ ri, ⌊err0⌋ , ¬ fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].directory, ¬ dentrykey(m, str0) ∈ ri, asynced → boolvar0, links(fs[ri[dentrykey(ino2, str)]].ino, abs-dirs(fs, ri)) ≠ ∅ ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs[ri[inodekey(ino2)]].nlink ≠ 0 ∨ ino2 = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink ≠ 0 ∨ fs[ri[dentrykey(ino2, str)]].ino = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, fs[ri[dentrykey(ino2, str)]].ino); p_inode0, p_inode1, old_dent0, err1, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = p_inode0 ∧ mkinode(fs[ri[dentrykey(ino2, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink, 0, m6) = p_inode1 ∧ negdentry(str0) = old_dent0 ∧ err0 = err1), fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(ino2, str)]].ino)]].nlink = 0 ∧ fs[ri[dentrykey(ino2, str)]].ino ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs[ri[inodekey(m)]], key0, md1, boolvar1, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs[ri[inodekey(m)]], key0, md1, boolvar1, m0, m1, m2