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Proof step 5 from proof inv-rename-overwrite-keep-parent (previous step)

fs[ri[dentrykey(parent_inode.ino, str)]].ino = old_child_inode.ino, new_child_inode.ino = new_dent.ino, fs[ri[dentrykey(parent_inode.ino, new_dent.name)]].ino = new_dent.ino, parent_inode.nlink = fs[ri[inodekey(parent_inode.ino)]].nlink, parent_inode.nsubdirs = fs[ri[inodekey(parent_inode.ino)]].nsubdirs, parent_inode.size = fs[ri[inodekey(parent_inode.ino)]].size, ¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory, old_dent = mkdentry(str, old_child_inode.ino), new_dent.ino ≠ ROOT_INO, new_child_inode.nlink ≠ 0, parent_inode.size ≠ 0, new_dent.dentry?, parent_inode.directory, fs[ri[inodekey(parent_inode.ino)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), dentrykey(parent_inode.ino, str) ∈ ri, inodekey(old_child_inode.ino) ∈ ri, dentrykey(parent_inode.ino, new_dent.name) ∈ ri, inodekey(new_dent.ino) ∈ ri, inodekey(parent_inode.ino) ∈ ri, 1 ≤ parent_inode.size, ¬ inodekey(parent_inode.ino) ∈ ro, old_child_inode.directory → 1 ≤ parent_inode.nsubdirs, new_child_inode.nlink = 1 → links(new_dent.ino, fs, ri) = ∅ ++ dentrykey(parent_inode.ino, new_dent.name), fs[ri[inodekey(new_dent.ino)]].directory → dentrykeys(inodekey(new_dent.ino), ri) = ∅, parent_inode.nlink ≠ 0 ∨ parent_inode.ino = ROOT_INO, ¬ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ ¬ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_child_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_child_inode.ino)]].nsubdirs ∧ old_child_inode.size = fs[ri[inodekey(old_child_inode.ino)]].size, ¬ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ ¬ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_dent.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∨ fs[ri[inodekey(new_dent.ino)]].directory ∧ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_dent.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ new_child_inode.size = fs[ri[inodekey(new_dent.ino)]].size ⊦ ⟪aubifs_rename_overwrite_keep_parent# (old_child_inode.directory, old_child_inode, fi, fo; parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
fs[ri[dentrykey(parent_inode.ino, str0)]].ino = m, new_child_inode.ino = m, fs[ri[dentrykey(parent_inode.ino, str)]].ino = old_child_inode.ino, parent_inode.nlink = fs[ri[inodekey(parent_inode.ino)]].nlink, parent_inode.nsubdirs = fs[ri[inodekey(parent_inode.ino)]].nsubdirs, parent_inode.size = fs[ri[inodekey(parent_inode.ino)]].size, ¬ fs[ri[inodekey(m)]].directory ↔ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory, new_dent = mkdentry(str0, m), old_dent = mkdentry(str, old_child_inode.ino), new_dent.dentry?, fs[ri[inodekey(parent_inode.ino)]].directory, parent_inode.directory, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(parent_inode.ino) ∈ ri, inodekey(m) ∈ ri, dentrykey(parent_inode.ino, str0) ∈ ri, inodekey(old_child_inode.ino) ∈ ri, dentrykey(parent_inode.ino, str) ∈ ri, 1 ≤ parent_inode.size, fs[ri[inodekey(m)]].directory → dentrykeys(inodekey(m), ri) = ∅, new_child_inode.nlink = 1 → links(m, fs, ri) = ∅ ++ dentrykey(parent_inode.ino, str0), old_child_inode.directory → 1 ≤ parent_inode.nsubdirs, ¬ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ ¬ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(m)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(m)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(m)]].nsubdirs ∧ new_child_inode.size = fs[ri[inodekey(m)]].size, ¬ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ ¬ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_child_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_child_inode.ino)]].nsubdirs ∧ old_child_inode.size = fs[ri[inodekey(old_child_inode.ino)]].size, parent_inode.nlink ≠ 0 ∨ parent_inode.ino = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_keep_parent# (old_child_inode.directory, old_child_inode, fi, fo; parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), new_child_inode.nlink = 0, parent_inode.size = 0, m = ROOT_INO, inodekey(parent_inode.ino) ∈ ro

Rule argument

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

Additional information

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