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Proof step 9 from proof inv-rename-overwrite-reparent (previous step)

fs[ri[dentrykey(m, str)]].ino = old_child_inode.ino, fs[ri[dentrykey(new_parent_inode.ino, str0)]].ino = new_child_inode.ino, new_parent_inode.nlink = fs[ri[inodekey(new_parent_inode.ino)]].nlink, new_parent_inode.nsubdirs = fs[ri[inodekey(new_parent_inode.ino)]].nsubdirs, new_parent_inode.size = fs[ri[inodekey(new_parent_inode.ino)]].size, ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ↔ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory, new_dent = mkdentry(str0, new_child_inode.ino), old_dent = mkdentry(str, old_child_inode.ino), old_parent_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), new_parent_inode.ino ≠ m, new_child_inode.ino ≠ ROOT_INO, new_child_inode.nlink ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, new_parent_inode.directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(new_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(m, str) ∈ ri, inodekey(old_child_inode.ino) ∈ ri, dentrykey(new_parent_inode.ino, str0) ∈ ri, inodekey(new_child_inode.ino) ∈ ri, inodekey(new_parent_inode.ino) ∈ ri, inodekey(m) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, ¬ inodekey(m) ∈ ro, ¬ inodekey(new_parent_inode.ino) ∈ ro, old_child_inode.directory → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, new_child_inode.nlink = 1 → links(new_child_inode.ino, fs, ri) = ∅ ++ dentrykey(new_parent_inode.ino, str0), fs[ri[inodekey(new_child_inode.ino)]].directory → dentrykeys(inodekey(new_child_inode.ino), ri) = ∅, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, new_parent_inode.nlink ≠ 0 ∨ new_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_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∧ new_child_inode.size = fs[ri[inodekey(new_child_inode.ino)]].size ⊦ ⟪aubifs_rename_overwrite_reparent# (old_child_inode.directory, old_child_inode, fi, fo ; old_parent_inode, new_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 10:
fs[ri[dentrykey(m0, str0)]].ino = new_child_inode.ino, fs[ri[dentrykey(m, str)]].ino = old_child_inode.ino, ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ↔ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory, boolvar, m1 = fs[ri[inodekey(m0)]].nlink, m2 = fs[ri[inodekey(m0)]].nsubdirs, m3 = fs[ri[inodekey(m0)]].size, new_dent = mkdentry(str0, new_child_inode.ino), new_parent_inode = mkinode(m0, md0, boolvar, m1, m2, m3), old_dent = mkdentry(str, old_child_inode.ino), old_parent_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(m)]].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(m) ∈ ri, inodekey(m0) ∈ ri, inodekey(new_child_inode.ino) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(old_child_inode.ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, fs[ri[inodekey(new_child_inode.ino)]].directory → dentrykeys(inodekey(new_child_inode.ino), ri) = ∅, new_child_inode.nlink = 1 → links(new_child_inode.ino, fs, ri) = ∅ ++ dentrykey(m0, str0), old_child_inode.directory → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ ¬ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∧ new_child_inode.size = fs[ri[inodekey(new_child_inode.ino)]].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, m1 ≠ 0 ∨ m0 = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_reparent# (old_child_inode.directory, old_child_inode, fi, fo ; old_parent_inode, new_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.ino = ROOT_INO, new_child_inode.nlink = 0, fs[ri[inodekey(m)]].size = 0, m0 = m, inodekey(m) ∈ ro, inodekey(m0) ∈ ro

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [new_parent_inode, m0, md0, boolvar, m1, m2, m3]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: new_parent_inode, m0, md0, boolvar, m1, m2, m3