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Proof step 1432 from proof refine-rename-overwrite-reparent-dir (previous step)

m16 + 1 = fs[ri[inodekey(m11)]].nsubdirs, m13 + 1 = fs[ri[inodekey(m11)]].size, m14 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nlink, abs-children(fs[ri[dentrykey(m7, str0)]].ino, fs, ri) = ∅, dentrykeys(inodekey(fs[ri[dentrykey(m7, str0)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode = mkinode (fs[ri[dentrykey(m7, str0)]].ino, md0, true, m14 + 1, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].size), new_inode = mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size), old_dent0 = mkdentry(str, fs[ri[dentrykey(m11, str)]].ino), old_dent1 = mkdentry(str0, fs[ri[dentrykey(m7, str0)]].ino), old_dent_inode = mkinode (fs[ri[dentrykey(m11, str)]].ino, md, true, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].nlink, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].size), old_inode = mkinode(m11, md2, true, fs[ri[inodekey(m11)]].nlink, m16 + 1, m13 + 1), fs[ri[dentrykey(m7, str0)]].ino ≠ 0, fs[ri[dentrykey(m7, str0)]].ino ≠ ROOT_INO, m11 ≠ 0, m11 ≠ m7, m7 ≠ 0, fs[ri[dentrykey(m7, str0)]].dentry?, fs[ri[dentrykey(m11, str)]].dentry?, fs[ri[inodekey(m11)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].directory, fs[ri[inodekey(m7)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].inode?, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].inode?, fs[ri[inodekey(m7)]].inode?, fs[ri[inodekey(m11)]].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(fs[ri[dentrykey(m11, str)]].ino) ∈ ri, ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(fs[ri[dentrykey(m7, str0)]].ino) ∈ ri, ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)] ∈ fs, ri[dentrykey(m7, str0)] ∈ fs, dentrykey(m7, str0) ∈ ri, ri[inodekey(m11)] ∈ fs, inodekey(m11) ∈ ri, ri[dentrykey(m11, str)] ∈ fs, dentrykey(m11, str) ∈ ri, ⌊err0⌋ , boolvar2 → boolvar0, m14 = 0 → links(fs[ri[dentrykey(m7, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m7, str0), fs[ri[inodekey(m11)]].nlink ≠ 0 ∨ m11 = ROOT_INO, fs[ri[inodekey(m7)]].nlink ≠ 0 ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs, ri)) ≠ ∅ ∨ m11 = ROOT_INO, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err1, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar2 → boolvar1) ∧ mkinode(m11, md2, true, fs[ri[inodekey(m11)]].nlink, m16 + 1, m13 + 1) = old_inode ∧ mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size) = new_inode ∧ mkinode (fs[ri[dentrykey(m11, str)]].ino, md, true, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].nlink, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m11, str)]].ino)]].size) = old_dent_inode ∧ mkinode (fs[ri[dentrykey(m7, str0)]].ino, md0, true, m14 + 1, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].size) = new_dent_inode ∧ mkdentry(str, fs[ri[dentrykey(m11, str)]].ino) = old_dent0 ∧ mkdentry(str0, fs[ri[dentrykey(m7, str0)]].ino) = old_dent1 ∧ err0 = err1), fs[ri[inodekey(m7)]].nlink = 0 ∧ m7 ≠ ROOT_INO, fs[ri[inodekey(m11)]].nlink = 0 ∧ m11 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1433:
m14 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nlink, m13 + 1 = fs[ri[inodekey(m11)]].size, m16 + 1 = fs[ri[inodekey(m11)]].nsubdirs, fs[ri[dentrykey(m11, str)]] = dentrynode(key, m), abs-children(fs[ri[dentrykey(m7, str0)]].ino, fs, ri) = ∅, dentrykeys(inodekey(fs[ri[dentrykey(m7, str0)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode = mkinode (fs[ri[dentrykey(m7, str0)]].ino, md0, true, m14 + 1, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].size), new_inode = mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, fs[ri[dentrykey(m7, str0)]].ino), old_dent_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), old_inode = mkinode(m11, md2, true, fs[ri[inodekey(m11)]].nlink, m16 + 1, m13 + 1), fs[ri[dentrykey(m11, str)]].dentry?, fs[ri[dentrykey(m7, str0)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m7)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].directory, fs[ri[inodekey(m11)]].directory, fs[ri[inodekey(m11)]].inode?, fs[ri[inodekey(m7)]].inode?, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].inode?, 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(m11, str) ∈ ri, ri[dentrykey(m11, str)] ∈ fs, inodekey(m11) ∈ ri, ri[inodekey(m11)] ∈ fs, dentrykey(m7, str0) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)] ∈ fs, inodekey(fs[ri[dentrykey(m7, str0)]].ino) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, ⌊err0⌋ , m14 = 0 → links(fs[ri[dentrykey(m7, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar2 → boolvar0, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs, ri)) ≠ ∅ ∨ m11 = ROOT_INO, fs[ri[inodekey(m7)]].nlink ≠ 0 ∨ m7 = ROOT_INO, fs[ri[inodekey(m11)]].nlink ≠ 0 ∨ m11 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err1, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar2 → boolvar1) ∧ mkinode(m11, md2, true, fs[ri[inodekey(m11)]].nlink, m16 + 1, m13 + 1) = old_inode ∧ mkinode(m7, md1, true, fs[ri[inodekey(m7)]].nlink, fs[ri[inodekey(m7)]].nsubdirs, fs[ri[inodekey(m7)]].size) = new_inode ∧ mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size) = old_dent_inode ∧ mkinode (fs[ri[dentrykey(m7, str0)]].ino, md0, true, m14 + 1, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].size) = new_dent_inode ∧ mkdentry(str, m) = old_dent0 ∧ mkdentry(str0, fs[ri[dentrykey(m7, str0)]].ino) = old_dent1 ∧ err0 = err1), fs[ri[dentrykey(m7, str0)]].ino = 0, fs[ri[dentrykey(m7, str0)]].ino = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, fs[ri[inodekey(m11)]].nlink = 0 ∧ m11 ≠ ROOT_INO, fs[ri[inodekey(m7)]].nlink = 0 ∧ m7 ≠ ROOT_INO

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(m11, str)]], key, m]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[dentrykey(m11, str)]], key, m