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Proof step 15 from proof refine-rename-overwrite-reparent-file (previous step)

old_inode.nlink = fs[ri[inodekey(old_inode.ino)]].nlink, old_inode.nsubdirs = fs[ri[inodekey(old_inode.ino)]].nsubdirs, old_inode.size = fs[ri[inodekey(old_inode.ino)]].size, 0 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nsubdirs, 0 = fs[ri[inodekey(fs[ri[dentrykey(old_inode.ino, str)]].ino)]].nsubdirs, 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[dentrykey(m4, str0)]].ino, m3 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink, m6 = fs[ri[inodekey(m4)]].nlink, m7 = fs[ri[inodekey(m4)]].nsubdirs, m8 = fs[ri[inodekey(m4)]].size, new_child_inode = mkinode(fs[ri[dentrykey(m4, str0)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink, 0, m5), new_dent = mkdentry(str0, fs[ri[dentrykey(m4, str0)]].ino), new_parent_inode = mkinode(m4, md1, true, fs[ri[inodekey(m4)]].nlink, fs[ri[inodekey(m4)]].nsubdirs, fs[ri[inodekey(m4)]].size), old_dent = mkdentry(str, fs[ri[dentrykey(old_inode.ino, str)]].ino), old_parent_inode = old_inode, ro = orphans(fs, ri), old_inode.ino ≠ m4, fs[ri[dentrykey(m4, str0)]].ino ≠ ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink ≠ 0, old_inode.size ≠ 0, old_inode.directory, fs[ri[inodekey(old_inode.ino)]].directory, fs[ri[inodekey(m4)]].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(m4, str0)]].ino) ∈ ri, dentrykey(m4, str0) ∈ ri, inodekey(m4) ∈ ri, 1 ≤ old_inode.size, ¬ fs[ri[inodekey(fs[ri[dentrykey(old_inode.ino, str)]].ino)]].directory, ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].directory, boolvar → boolvar0, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m4, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m4, str0), links(old_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ old_inode.ino = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, old_inode.nlink ≠ 0 ∨ old_inode.ino = ROOT_INO, fs[ri[inodekey(m4)]].nlink ≠ 0 ∨ m4 = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_reparent# (false, mkinode(m, md, false, m0, 0, 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, false, m0, 0, m2); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m1); old_dent_inode := mkinode(m, md, false, m0, 0, m2); new_dent_inode := mkinode(m1, md0, false, m3, 0, m5); new_inode := mkinode(m4, md1, true, m6, m7, m8); 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), fs[ri[inodekey(m4)]].nlink = 0 ∧ m4 ≠ 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] → [old_inode, m9, md2, boolvar1, m10, m11, m12]

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, m9, md2, boolvar1, m10, m11, m12