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Proof step 38 from proof refine-rename-overwrite-reparent (previous step)

⟨afs_rename#(; old_inode, new_inode, old_child_inode0, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( old_inode = old_inode0 ∧ new_inode = new_inode0 ∧ old_child_inode0 = mkinode(fs[ri[dentrykey(m0, str)]].ino, md, false, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, 0, m2) ∧ 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)), 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, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode = mkinode(fs[ri[dentrykey(new_inode.ino, str0)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].nlink, 0, m4), old_child_inode0 = mkinode(fs[ri[dentrykey(m0, str)]].ino, md, false, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, 0, m2), old_dent0 = mkdentry(str, fs[ri[dentrykey(m0, str)]].ino), old_dent1 = mkdentry(str0, fs[ri[dentrykey(new_inode.ino, str0)]].ino), old_inode = mkinode(m0, md1, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), orphans(abs-dirs(fs0, ri0), abs-files(fs0, ri0)) = abs-keys(ro0), m0 ≠ new_inode.ino, new_inode.directory, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(new_inode.ino)]].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(m0, str) ∈ ri, inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino) ∈ ri, dentrykey(new_inode.ino, str0) ∈ ri, inodekey(new_inode.ino) ∈ ri, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ri, inodekey(m0) ∈ ri, ¬ fs[ri[inodekey(fs[ri[dentrykey(new_inode.ino, str0)]].ino)]].directory, ¬ fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].directory, boolvar1 → boolvar2, boolvar → boolvar0, links(m0, abs-dirs(fs, ri)) ≠ ∅ ∨ m0 = 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 ∧ mkinode(fs[ri[dentrykey(m0, str)]].ino, md, false, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, 0, m2) = 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 39:
⟨afs_rename#(; old_inode, new_inode, old_child_inode0, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( old_inode = old_inode0 ∧ new_inode = new_inode0 ∧ old_child_inode0 = mkinode(fs[ri[dentrykey(m0, str)]].ino, md, false, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, 0, m2) ∧ 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)), boolvar3, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), m1 = fs[ri[inodekey(m)]].nlink, m3 = fs[ri[inodekey(m)]].nsubdirs, m5 = fs[ri[inodekey(m)]].size, new_dent_inode = mkinode(fs[ri[dentrykey(m, str0)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink, 0, m4), new_inode = mkinode(m, md2, boolvar3, m1, m3, m5), old_child_inode0 = mkinode(fs[ri[dentrykey(m0, str)]].ino, md, false, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, 0, m2), old_dent0 = mkdentry(str, fs[ri[dentrykey(m0, str)]].ino), old_dent1 = mkdentry(str0, fs[ri[dentrykey(m, str0)]].ino), old_inode = mkinode(m0, md1, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), orphans(abs-dirs(fs0, ri0), abs-files(fs0, ri0)) = abs-keys(ro0), fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m0)]].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(m0) ∈ ri, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ri, inodekey(m) ∈ ri, dentrykey(m, str0) ∈ ri, inodekey(fs[ri[dentrykey(m, str0)]].ino) ∈ ri, dentrykey(m0, str) ∈ ri, boolvar → boolvar0, boolvar1 → boolvar2, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(m0, abs-dirs(fs, ri)) ≠ ∅ ∨ m0 = 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 ∧ mkinode(fs[ri[dentrykey(m0, str)]].ino, md, false, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, 0, m2) = old_child_inode0 ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ old_dent2 = old_dent1 ∧ err = err0), m0 = m, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].directory

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, m, md2, boolvar3, m1, m3, 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: new_inode, m, md2, boolvar3, m1, m3, m5