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

⟨afs_rename#(; old_inode, new_inode, old_child_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( old_inode = old_inode0 ∧ new_inode = new_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_dent_inode = new_dent_inode0 ∧ old_dent0 = old_dent ∧ old_dent1 = old_dent2 ∧ err0 = err ∧ dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ (boolvar ↔ boolvar1)), old_child_inode0.ino = fs[ri[dentrykey(old_inode.ino, str)]].ino, new_dent_inode.ino = fs[ri[dentrykey(new_inode.ino, str0)]].ino, new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, old_inode.nlink = fs[ri[inodekey(old_inode.ino)]].nlink, new_dent_inode.nlink = fs[ri[inodekey(new_dent_inode.ino)]].nlink, old_child_inode0.nlink = fs[ri[inodekey(old_child_inode0.ino)]].nlink, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, old_inode.nsubdirs = fs[ri[inodekey(old_inode.ino)]].nsubdirs, new_dent_inode.nsubdirs = fs[ri[inodekey(new_dent_inode.ino)]].nsubdirs, old_child_inode0.nsubdirs = fs[ri[inodekey(old_child_inode0.ino)]].nsubdirs, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, old_inode.size = fs[ri[inodekey(old_inode.ino)]].size, new_dent_inode.size = fs[ri[inodekey(new_dent_inode.ino)]].size, old_child_inode0.size = fs[ri[inodekey(old_child_inode0.ino)]].size, abs-children(new_dent_inode.ino, fs, ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), old_child_inode = old_child_inode0, old_dent0 = mkdentry(str, old_child_inode0.ino), old_dent1 = mkdentry(str0, new_dent_inode.ino), orphans(abs-dirs(fs0, ri0), abs-files(fs0, ri0)) = abs-keys(ro0), new_dent_inode.ino ≠ ROOT_INO, old_inode.ino ≠ new_inode.ino, new_inode.directory, old_inode.directory, fs[ri[inodekey(old_inode.ino)]].directory, fs[ri[inodekey(new_dent_inode.ino)]].directory, fs[ri[inodekey(new_inode.ino)]].directory, new_dent_inode.directory, fs[ri[inodekey(old_child_inode0.ino)]].directory, old_child_inode0.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(old_inode.ino, str) ∈ ri, inodekey(old_inode.ino) ∈ ri, inodekey(new_dent_inode.ino) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, inodekey(new_inode.ino) ∈ ri, inodekey(old_child_inode0.ino) ∈ ri, boolvar1 → boolvar2, boolvar → boolvar0, 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 ⊦ ⟨afs_rename#(; old_inode, new_inode, old_child_inode0, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ (boolvar → boolvar2) ∧ old_inode0 = old_inode ∧ new_inode0 = new_inode ∧ old_child_inode = old_child_inode0 ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ old_dent2 = old_dent1 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
⟨afs_rename#(; old_inode, new_inode, old_child_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( old_inode = old_inode0 ∧ new_inode = new_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_dent_inode = new_dent_inode0 ∧ old_dent0 = old_dent ∧ old_dent1 = old_dent2 ∧ err0 = err ∧ dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ (boolvar ↔ boolvar1)), old_child_inode0.ino = fs[ri[dentrykey(old_inode.ino, str)]].ino, old_child_inode0.nlink = fs[ri[inodekey(old_child_inode0.ino)]].nlink, old_inode.nlink = fs[ri[inodekey(old_inode.ino)]].nlink, new_inode.nlink = fs[ri[inodekey(new_inode.ino)]].nlink, old_child_inode0.nsubdirs = fs[ri[inodekey(old_child_inode0.ino)]].nsubdirs, old_inode.nsubdirs = fs[ri[inodekey(old_inode.ino)]].nsubdirs, new_inode.nsubdirs = fs[ri[inodekey(new_inode.ino)]].nsubdirs, old_child_inode0.size = fs[ri[inodekey(old_child_inode0.ino)]].size, old_inode.size = fs[ri[inodekey(old_inode.ino)]].size, new_inode.size = fs[ri[inodekey(new_inode.ino)]].size, abs-children(m, fs, ri) = ∅, boolvar3, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), m = fs[ri[dentrykey(new_inode.ino, str0)]].ino, m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, new_dent_inode = mkinode(m, md, boolvar3, m0, m1, m2), old_child_inode = old_child_inode0, old_dent0 = mkdentry(str, old_child_inode0.ino), old_dent1 = mkdentry(str0, m), orphans(abs-dirs(fs0, ri0), abs-files(fs0, ri0)) = abs-keys(ro0), old_child_inode0.directory, fs[ri[inodekey(old_child_inode0.ino)]].directory, fs[ri[inodekey(new_inode.ino)]].directory, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(old_inode.ino)]].directory, old_inode.directory, new_inode.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(old_child_inode0.ino) ∈ ri, inodekey(new_inode.ino) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, inodekey(m) ∈ ri, inodekey(old_inode.ino) ∈ ri, dentrykey(old_inode.ino, str) ∈ ri, boolvar → boolvar0, boolvar1 → boolvar2, links(new_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ new_inode.ino = ROOT_INO, links(old_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ old_inode.ino = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_child_inode0, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ (boolvar → boolvar2) ∧ old_inode0 = old_inode ∧ new_inode0 = new_inode ∧ old_child_inode = old_child_inode0 ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ old_dent2 = old_dent1 ∧ err = err0), old_inode.ino = new_inode.ino, m = 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_dent_inode, m, md, boolvar3, 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: new_dent_inode, m, md, boolvar3, m0, m1, m2