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Proof step 13 from proof refine-rename-overwrite-reparent-dir (previous step)

new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, old_inode.nlink = fs[ri[inodekey(old_inode.ino)]].nlink, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, old_inode.nsubdirs = fs[ri[inodekey(old_inode.ino)]].nsubdirs, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, old_inode.size = fs[ri[inodekey(old_inode.ino)]].size, abs-children(fs[ri[dentrykey(new_inode.ino, str0)]].ino, fs, ri) = ∅, dentrykeys(inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), m = fs[ri[dentrykey(old_inode.ino, str)]].ino, m0 = fs[ri[inodekey(fs[ri[dentrykey(old_inode.ino, str)]].ino)]].nlink, m1 = fs[ri[inodekey(fs[ri[dentrykey(old_inode.ino, str)]].ino)]].nsubdirs, m2 = fs[ri[inodekey(fs[ri[dentrykey(old_inode.ino, str)]].ino)]].size, m3 = fs[ri[dentrykey(new_inode.ino, str0)]].ino, m4 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nlink, m5 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nsubdirs, m6 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].size, new_child_inode = mkinode (fs[ri[dentrykey(new_inode.ino, str0)]].ino, md0, true, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nlink, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].size), new_dent = mkdentry(str0, fs[ri[dentrykey(new_inode.ino, str0)]].ino), new_parent_inode = new_inode, old_dent = mkdentry(str, fs[ri[dentrykey(old_inode.ino, str)]].ino), old_parent_inode = old_inode, ro = orphans(fs, ri), fs[ri[dentrykey(new_inode.ino, str0)]].ino ≠ ROOT_INO, old_inode.ino ≠ new_inode.ino, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nlink ≠ 0, old_inode.nsubdirs ≠ 0, old_inode.size ≠ 0, new_inode.directory, old_inode.directory, fs[ri[inodekey(old_inode.ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].directory, fs[ri[inodekey(new_inode.ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(old_inode.ino, str)]].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(fs[ri[dentrykey(old_inode.ino, str)]].ino) ∈ ri, dentrykey(old_inode.ino, str) ∈ ri, inodekey(old_inode.ino) ∈ ri, inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, inodekey(new_inode.ino) ∈ ri, 1 ≤ old_inode.size, 1 ≤ old_inode.nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(new_inode.ino, str0)]].ino, 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, mkinode(m, md, true, m0, m1, m2), fi, fo ; old_parent_inode, new_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ ⟨old_dent_inode0 := mkinode(m, md, true, m0, m1, m2); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m3); old_dent_inode := mkinode(m, md, true, m0, m1, m2); new_dent_inode := mkinode(m3, md0, true, m4, m5, m6); 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), new_inode.nlink = 0 ∧ new_inode.ino ≠ ROOT_INO, old_inode.nlink = 0 ∧ old_inode.ino ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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_inode, m7, md1, boolvar1, m8, m9, m10]

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_inode, m7, md1, boolvar1, m8, m9, m10