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Proof step 7 from proof refine-rename-overwrite-reparent-dir (previous step)

old_dent_inode.ino = fs[ri[dentrykey(old_inode.ino, str)]].ino, old_dent1.ino = fs[ri[dentrykey(new_inode.ino, old_dent1.name)]].ino, new_dent_inode.ino = old_dent1.ino, old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink, old_inode.nlink = fs[ri[inodekey(old_inode.ino)]].nlink, new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, new_dent_inode.nlink = fs[ri[inodekey(old_dent1.ino)]].nlink, old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs, old_inode.nsubdirs = fs[ri[inodekey(old_inode.ino)]].nsubdirs, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, new_dent_inode.nsubdirs = fs[ri[inodekey(old_dent1.ino)]].nsubdirs, old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size, old_inode.size = fs[ri[inodekey(old_inode.ino)]].size, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, new_dent_inode.size = fs[ri[inodekey(old_dent1.ino)]].size, abs-children(old_dent1.ino, fs, ri) = ∅, dentrykeys(inodekey(old_dent1.ino), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent1, new_parent_inode = new_inode, old_dent = mkdentry(str, old_dent_inode.ino), old_parent_inode = old_inode, ro = orphans(fs, ri), old_dent1.ino ≠ ROOT_INO, old_inode.ino ≠ new_inode.ino, new_dent_inode.nlink ≠ 0, old_inode.nsubdirs ≠ 0, old_inode.size ≠ 0, old_dent1.dentry?, old_dent_inode.directory, fs[ri[inodekey(old_dent_inode.ino)]].directory, new_dent_inode.directory, fs[ri[inodekey(new_inode.ino)]].directory, fs[ri[inodekey(old_dent1.ino)]].directory, fs[ri[inodekey(old_inode.ino)]].directory, old_inode.directory, new_inode.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(new_inode.ino) ∈ ri, dentrykey(new_inode.ino, old_dent1.name) ∈ ri, inodekey(old_dent1.ino) ∈ ri, inodekey(old_inode.ino) ∈ ri, dentrykey(old_inode.ino, str) ∈ ri, inodekey(old_dent_inode.ino) ∈ ri, 1 ≤ old_inode.nsubdirs, 1 ≤ old_inode.size, boolvar → boolvar0, new_dent_inode.nlink = 1 → links(old_dent1.ino, fs, ri) = ∅ ++ dentrykey(new_inode.ino, old_dent1.name), links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO, links(old_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ old_inode.ino = ROOT_INO, new_inode.nlink ≠ 0 ∨ new_inode.ino = ROOT_INO, old_inode.nlink ≠ 0 ∨ old_inode.ino = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_reparent# (true, old_dent_inode, fi, fo; old_parent_inode, new_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ ⟨old_dent_inode0 := old_dent_inode; old_dent0 := mkdentry(str, old_dent_inode.ino); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (boolvar → boolvar0) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), old_inode.nlink = 0 ∧ old_inode.ino ≠ ROOT_INO, new_inode.nlink = 0 ∧ new_inode.ino ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
new_dent_inode.ino = m, old_dent_inode.ino = fs[ri[dentrykey(old_inode.ino, str)]].ino, new_dent_inode.nlink = fs[ri[inodekey(m)]].nlink, new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, old_inode.nlink = fs[ri[inodekey(old_inode.ino)]].nlink, old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink, new_dent_inode.nsubdirs = fs[ri[inodekey(m)]].nsubdirs, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, old_inode.nsubdirs = fs[ri[inodekey(old_inode.ino)]].nsubdirs, old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs, new_dent_inode.size = fs[ri[inodekey(m)]].size, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, old_inode.size = fs[ri[inodekey(old_inode.ino)]].size, old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size, abs-children(m, fs, ri) = ∅, dentrykeys(inodekey(m), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), m = fs[ri[dentrykey(new_inode.ino, str0)]].ino, new_child_inode = new_dent_inode, new_dent = old_dent1, new_parent_inode = new_inode, old_dent = mkdentry(str, old_dent_inode.ino), old_dent1 = mkdentry(str0, m), old_parent_inode = old_inode, ro = orphans(fs, ri), old_dent1.dentry?, new_inode.directory, old_inode.directory, fs[ri[inodekey(old_inode.ino)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(new_inode.ino)]].directory, new_dent_inode.directory, fs[ri[inodekey(old_dent_inode.ino)]].directory, old_dent_inode.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), inodekey(old_dent_inode.ino) ∈ ri, dentrykey(old_inode.ino, str) ∈ ri, inodekey(old_inode.ino) ∈ ri, inodekey(m) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, inodekey(new_inode.ino) ∈ ri, 1 ≤ old_inode.size, 1 ≤ old_inode.nsubdirs, new_dent_inode.nlink = 1 → links(m, fs, ri) = ∅ ++ dentrykey(new_inode.ino, str0), boolvar → boolvar0, old_inode.nlink ≠ 0 ∨ old_inode.ino = ROOT_INO, new_inode.nlink ≠ 0 ∨ new_inode.ino = ROOT_INO, links(old_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ old_inode.ino = ROOT_INO, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_reparent# (true, old_dent_inode, fi, fo; old_parent_inode, new_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ ⟨old_dent_inode0 := old_dent_inode; old_dent0 := mkdentry(str, old_dent_inode.ino); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (boolvar → boolvar0) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), old_inode.ino = new_inode.ino, new_dent_inode.nlink = 0, old_inode.nsubdirs = 0, old_inode.size = 0, m = ROOT_INO, new_inode.nlink = 0 ∧ new_inode.ino ≠ ROOT_INO, old_inode.nlink = 0 ∧ old_inode.ino ≠ ROOT_INO

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [old_dent1, str0, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: old_dent1, str0, m