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Proof step 571 from proof refine-unlink (previous step)

m5 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, 0 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), 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(m, str)]].ino, md0, false, m5 + 1, 0, m6), fs[ri[dentrykey(m, str)]].ino ≠ ROOT_INO, fs[ri[dentrykey(m, str)]].ino ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, m ≠ 0, fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m)]].inode?, 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-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, ri[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, ⌊err0⌋ , ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, m5 = 0 → links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), asynced → boolvar0, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_unlink#(; p_inode0, p_inode1, old_dent, 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(m, str)]].ino, md0, false, m5 + 1, 0, m6) = p_inode1 ∧ mkdentry(str, fs[ri[dentrykey(m, str)]].ino) = old_dent ∧ err0 = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 572:
m5 + 1 = fs[ri[inodekey(m0)]].nlink, 0 = fs[ri[inodekey(m0)]].nsubdirs, fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), old_dent = mkdentry(str, m0), p_inode0 = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), p_inode1 = mkinode(m0, md0, false, m5 + 1, 0, m6), fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m)]].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), dentrykey(m, str) ∈ ri, ri[dentrykey(m, str)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, ⌊err0⌋ , asynced → boolvar0, m5 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m, str), fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_unlink#(; p_inode0, p_inode1, old_dent, 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(m0, md0, false, m5 + 1, 0, m6) = p_inode1 ∧ mkdentry(str, m0) = old_dent ∧ err0 = err1), fs[ri[inodekey(m)]].size = 0, m = 0, m0 = ROOT_INO, m0 = 0, fs[ri[inodekey(m0)]].directory

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs[ri[dentrykey(m, str)]], key, m0]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[dentrykey(m, str)]], key, m0