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Proof step 9 from proof refine-rename-overwrite-keep-parent-identity (previous step)

old_dent_inode.ino = fs[ri[dentrykey(new_inode.ino, str)]].ino, old_inode.ino = new_inode.ino, new_inode.meta = old_inode.meta, new_inode.nlink = old_inode.nlink, old_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, new_inode.nsubdirs = old_inode.nsubdirs, old_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, new_inode.size = old_inode.size, old_inode.size = fs[ri[inodekey(new_inode.ino)]].size, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = mkinode(old_dent_inode.ino, md, boolvar1, m0, m1, m2), new_dent = mkdentry(str, old_dent_inode.ino), old_dent = mkdentry(str, old_dent_inode.ino), old_parent_inode = old_inode, ro = orphans(fs, ri), old_dent_inode.ino ≠ ROOT_INO, old_inode.size ≠ 0, m0 ≠ 0, new_inode.directory, old_inode.directory, fs[ri[inodekey(new_inode.ino)]].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(new_inode.ino) ∈ ri, inodekey(old_dent_inode.ino) ∈ ri, dentrykey(new_inode.ino, str) ∈ ri, 1 ≤ old_inode.size, old_dent_inode.directory → 1 ≤ old_inode.nsubdirs, m0 = 1 → links(old_dent_inode.ino, fs, ri) = ∅ ++ dentrykey(new_inode.ino, str), boolvar → boolvar0, fs[ri[inodekey(old_dent_inode.ino)]].directory → abs-children(old_dent_inode.ino, fs, ri) = ∅, fs[ri[inodekey(old_dent_inode.ino)]].directory → dentrykeys(inodekey(old_dent_inode.ino), ri) = ∅, old_inode.nlink ≠ 0 ∨ new_inode.ino = ROOT_INO, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO, ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ ¬ old_dent_inode.directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size, ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m1 = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m1 = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(old_dent_inode.ino)]].size, fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ old_dent_inode.directory ∨ ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = 0 ∧ ¬ old_dent_inode.directory, fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m2 = fs[ri[inodekey(old_dent_inode.ino)]].size ∧ m1 = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ ⟪aubifs_rename_overwrite_keep_parent# (old_dent_inode.directory, old_dent_inode, fi, fo; old_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0); new_parent_inode := old_parent_inode⟫ ⟨old_dent2 := mkdentry(str, old_dent_inode.ino); old_dent_inode0 := old_dent_inode; old_dent1 := mkdentry(str, old_dent_inode.ino); new_dent_inode := mkinode(old_dent_inode.ino, md, boolvar1, m0, m1, m2); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent1, old_dent2, 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_dent1 ∧ new_dent = old_dent2 ∧ err = err0), old_inode.nlink = 0 ∧ new_inode.ino ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
old_dent_inode.ino = fs[ri[dentrykey(new_inode.ino, str)]].ino, new_inode.meta = md0, new_inode.nlink = m3, new_inode.nsubdirs = m4, new_inode.size = m5, boolvar2, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), m = new_inode.ino, m3 = fs[ri[inodekey(new_inode.ino)]].nlink, m4 = fs[ri[inodekey(new_inode.ino)]].nsubdirs, m5 = fs[ri[inodekey(new_inode.ino)]].size, new_child_inode = mkinode(old_dent_inode.ino, md, boolvar1, m0, m1, m2), new_dent = mkdentry(str, old_dent_inode.ino), old_dent = mkdentry(str, old_dent_inode.ino), old_inode = mkinode(m, md0, boolvar2, m3, m4, m5), old_parent_inode = old_inode, ro = orphans(fs, ri), fs[ri[inodekey(new_inode.ino)]].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), dentrykey(new_inode.ino, str) ∈ ri, inodekey(old_dent_inode.ino) ∈ ri, inodekey(new_inode.ino) ∈ ri, 1 ≤ m5, fs[ri[inodekey(old_dent_inode.ino)]].directory → dentrykeys(inodekey(old_dent_inode.ino), ri) = ∅, fs[ri[inodekey(old_dent_inode.ino)]].directory → abs-children(old_dent_inode.ino, fs, ri) = ∅, boolvar → boolvar0, m0 = 1 → links(old_dent_inode.ino, fs, ri) = ∅ ++ dentrykey(new_inode.ino, str), old_dent_inode.directory → 1 ≤ m4, fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m2 = fs[ri[inodekey(old_dent_inode.ino)]].size ∧ m1 = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ old_dent_inode.directory ∨ ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = 0 ∧ ¬ old_dent_inode.directory, ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m1 = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ m1 = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(old_dent_inode.ino)]].size, ¬ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ ¬ old_dent_inode.directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_dent_inode.ino)]].directory ∧ old_dent_inode.directory ∧ old_dent_inode.nlink = fs[ri[inodekey(old_dent_inode.ino)]].nlink ∧ old_dent_inode.nsubdirs = fs[ri[inodekey(old_dent_inode.ino)]].nsubdirs ∧ old_dent_inode.size = fs[ri[inodekey(old_dent_inode.ino)]].size, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO, m3 ≠ 0 ∨ new_inode.ino = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_keep_parent# (old_dent_inode.directory, old_dent_inode, fi, fo; old_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0); new_parent_inode := old_parent_inode⟫ ⟨old_dent2 := mkdentry(str, old_dent_inode.ino); old_dent_inode0 := old_dent_inode; old_dent1 := mkdentry(str, old_dent_inode.ino); new_dent_inode := mkinode(old_dent_inode.ino, md, boolvar1, m0, m1, m2); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent1, old_dent2, 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_dent1 ∧ new_dent = old_dent2 ∧ err = err0), old_dent_inode.ino = ROOT_INO, m0 = 0, m5 = 0, m3 = 0 ∧ new_inode.ino ≠ ROOT_INO

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_inode, m, md0, boolvar2, m3, m4, m5]

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_inode, m, md0, boolvar2, m3, m4, m5