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Proof step 15 from proof refine-rename-overwrite-keep-parent-different (previous step)

new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].directory, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), m = fs[ri[dentrykey(new_inode.ino, str)]].ino, m3 = fs[ri[dentrykey(new_inode.ino, str0)]].ino, new_child_inode = mkinode(fs[ri[dentrykey(new_inode.ino, str0)]].ino, md0, boolvar2, m4, m5, m6), new_dent = mkdentry(str0, fs[ri[dentrykey(new_inode.ino, str0)]].ino), old_dent = mkdentry(str, fs[ri[dentrykey(new_inode.ino, str)]].ino), old_parent_inode = mkinode(new_inode.ino, new_inode.meta, true, new_inode.nlink, new_inode.nsubdirs, new_inode.size), ro = orphans(fs, ri), fs[ri[dentrykey(new_inode.ino, str0)]].ino ≠ ROOT_INO, new_inode.size ≠ 0, m4 ≠ 0, mkdentry(str, fs[ri[dentrykey(new_inode.ino, str)]].ino) ≠ mkdentry(str0, fs[ri[dentrykey(new_inode.ino, str0)]].ino), new_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(fs[ri[dentrykey(new_inode.ino, str)]].ino) ∈ ri, inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino) ∈ ri, dentrykey(new_inode.ino, str) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, inodekey(new_inode.ino) ∈ ri, 1 ≤ new_inode.size, boolvar1 → 1 ≤ new_inode.nsubdirs, m4 = 1 → links(fs[ri[dentrykey(new_inode.ino, str0)]].ino, fs, ri) = ∅ ++ dentrykey(new_inode.ino, str0), boolvar → boolvar0, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].directory → abs-children(fs[ri[dentrykey(new_inode.ino, str0)]].ino, fs, ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino), ri) = ∅, new_inode.nlink ≠ 0 ∨ new_inode.ino = ROOT_INO, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].directory ∧ ¬ boolvar2 ∧ 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 ∨ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].directory ∧ boolvar2 ∧ 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, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].directory ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].size ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str)]].ino)]].directory ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2 ⊦ ⟪aubifs_rename_overwrite_keep_parent# (boolvar1, mkinode(m, md, boolvar1, m0, m1, m2), 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_dent_inode0 := mkinode(m, md, boolvar1, m0, m1, m2); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m3); old_inode := mkinode(new_inode.ino, new_inode.meta, true, new_inode.nlink, new_inode.nsubdirs, new_inode.size); old_dent_inode := mkinode(m, md, boolvar1, m0, m1, m2); new_dent_inode := mkinode(m3, md0, boolvar2, 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
¬ fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].directory, boolvar3, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), m = fs[ri[dentrykey(m7, str)]].ino, m10 = fs[ri[inodekey(m7)]].size, m3 = fs[ri[dentrykey(m7, str0)]].ino, m8 = fs[ri[inodekey(m7)]].nlink, m9 = fs[ri[inodekey(m7)]].nsubdirs, new_child_inode = mkinode(fs[ri[dentrykey(m7, str0)]].ino, md0, boolvar2, m4, m5, m6), new_dent = mkdentry(str0, fs[ri[dentrykey(m7, str0)]].ino), new_inode = mkinode(m7, md1, boolvar3, m8, m9, m10), old_dent = mkdentry(str, fs[ri[dentrykey(m7, str)]].ino), old_parent_inode = mkinode(m7, md1, true, m8, m9, m10), ro = orphans(fs, ri), fs[ri[inodekey(m7)]].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), inodekey(m7) ∈ ri, dentrykey(m7, str0) ∈ ri, dentrykey(m7, str) ∈ ri, inodekey(fs[ri[dentrykey(m7, str0)]].ino) ∈ ri, inodekey(fs[ri[dentrykey(m7, str)]].ino) ∈ ri, 1 ≤ m10, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m7, str0)]].ino), ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].directory → abs-children(fs[ri[dentrykey(m7, str0)]].ino, fs, ri) = ∅, boolvar → boolvar0, m4 = 1 → links(fs[ri[dentrykey(m7, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar1 → 1 ≤ m9, fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].directory ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].size ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].directory ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2, fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].directory ∧ ¬ boolvar2 ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nlink ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].directory ∧ boolvar2 ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nlink ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].nsubdirs ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m7, str0)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m7, str)]].ino)]].size, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, m8 ≠ 0 ∨ m7 = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_keep_parent# (boolvar1, mkinode(m, md, boolvar1, m0, m1, m2), 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_dent_inode0 := mkinode(m, md, boolvar1, m0, m1, m2); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m3); old_inode := mkinode(m7, md1, true, m8, m9, m10); old_dent_inode := mkinode(m, md, boolvar1, m0, m1, m2); new_dent_inode := mkinode(m3, md0, boolvar2, 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), fs[ri[dentrykey(m7, str0)]].ino = ROOT_INO, m10 = 0, m4 = 0, mkdentry(str, fs[ri[dentrykey(m7, str)]].ino) = mkdentry(str0, fs[ri[dentrykey(m7, str0)]].ino), m8 = 0 ∧ m7 ≠ 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] → [new_inode, m7, md1, boolvar3, 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, boolvar3, m8, m9, m10