[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 7 from proof inv-rename-new-reparent (previous step)

fs[ri[dentrykey(old_parent_inode.ino, str)]].ino = old_child_inode.ino, old_parent_inode.nlink = fs[ri[inodekey(old_parent_inode.ino)]].nlink, new_parent_inode.nlink = fs[ri[inodekey(new_parent_inode.ino)]].nlink, old_parent_inode.nsubdirs = fs[ri[inodekey(old_parent_inode.ino)]].nsubdirs, new_parent_inode.nsubdirs = fs[ri[inodekey(new_parent_inode.ino)]].nsubdirs, old_parent_inode.size = fs[ri[inodekey(old_parent_inode.ino)]].size, new_parent_inode.size = fs[ri[inodekey(new_parent_inode.ino)]].size, new_dent = negdentry(str0), old_dent = mkdentry(str, old_child_inode.ino), new_parent_inode.ino ≠ old_parent_inode.ino, old_parent_inode.size ≠ 0, old_parent_inode.directory, new_parent_inode.directory, fs[ri[inodekey(old_parent_inode.ino)]].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(old_parent_inode.ino, str) ∈ ri, inodekey(old_child_inode.ino) ∈ ri, inodekey(old_parent_inode.ino) ∈ ri, inodekey(new_parent_inode.ino) ∈ ri, 1 ≤ old_parent_inode.size, ¬ inodekey(new_parent_inode.ino) ∈ ro, ¬ dentrykey(new_parent_inode.ino, str0) ∈ ri, ¬ inodekey(old_parent_inode.ino) ∈ ro, old_child_inode.directory → 1 ≤ old_parent_inode.nsubdirs, old_parent_inode.nlink ≠ 0 ∨ old_parent_inode.ino = 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 ⊦ ⟪aubifs_rename_new_reparent# (old_child_inode.directory, old_child_inode, fi, ro, fo; old_parent_inode, new_parent_inode, old_dent, new_dent, err, ri, 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 8:
fs[ri[dentrykey(m, str)]].ino = old_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, boolvar, m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, new_dent = negdentry(str0), old_dent = mkdentry(str, old_child_inode.ino), old_parent_inode = mkinode(m, md, boolvar, m0, m1, m2), fs[ri[inodekey(new_parent_inode.ino)]].directory, fs[ri[inodekey(m)]].directory, new_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(new_parent_inode.ino) ∈ ri, inodekey(m) ∈ ri, inodekey(old_child_inode.ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ m2, old_child_inode.directory → 1 ≤ m1, ¬ 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, new_parent_inode.nlink ≠ 0 ∨ new_parent_inode.ino = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_rename_new_reparent# (old_child_inode.directory, old_child_inode, fi, ro, fo; old_parent_inode, new_parent_inode, old_dent, new_dent, err, ri, 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_parent_inode.ino = m, m2 = 0, inodekey(new_parent_inode.ino) ∈ ro, dentrykey(new_parent_inode.ino, str0) ∈ ri, inodekey(m) ∈ 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] → [old_parent_inode, m, md, boolvar, m0, m1, m2]

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: old_parent_inode, m, md, boolvar, m0, m1, m2