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Proof step 27 from proof refine-renam (previous step)

p_inode1.ino = fs[ri[dentrykey(p_inode0.ino, str)]].ino, p_inode.ino = p_inode0.ino, p_inode0.meta = p_inode.meta, p_inode0.nlink = p_inode.nlink, p_inode.nlink = fs[ri[inodekey(p_inode0.ino)]].nlink, p_inode0.nsubdirs = p_inode.nsubdirs, p_inode.nsubdirs = fs[ri[inodekey(p_inode0.ino)]].nsubdirs, p_inode0.size = p_inode.size, p_inode.size = fs[ri[inodekey(p_inode0.ino)]].size, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = p_inode2, new_dent = old_dent1, old_dent = mkdentry(str, p_inode1.ino), old_parent_inode = p_inode, ro = orphans(fs, ri), p_inode.size ≠ 0, old_dent1.dentry?, p_inode0.directory, fs[ri[inodekey(p_inode0.ino)]].directory, p_inode.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(p_inode0.ino) ∈ ri, inodekey(p_inode1.ino) ∈ ri, dentrykey(p_inode0.ino, str) ∈ ri, 1 ≤ p_inode.size, p_inode1.directory → 1 ≤ p_inode.nsubdirs, asynced → boolvar3, old_dent1.negdentry? ∧ ¬ dentrykey(p_inode0.ino, old_dent1.name) ∈ ri ∨ inodekey(old_dent1.ino) ∈ ri ∧ dentrykey(p_inode0.ino, old_dent1.name) ∈ ri ∧ fs[ri[dentrykey(p_inode0.ino, old_dent1.name)]].ino = old_dent1.ino ∧ ( inodekey(p_inode2.ino) ∈ ri ∧ ¬ fs[ri[inodekey(p_inode2.ino)]].directory ∧ ¬ p_inode2.directory ∧ p_inode2.nlink = fs[ri[inodekey(p_inode2.ino)]].nlink ∧ p_inode2.nsubdirs = fs[ri[inodekey(p_inode2.ino)]].nsubdirs ∨ inodekey(p_inode2.ino) ∈ ri ∧ fs[ri[inodekey(p_inode2.ino)]].directory ∧ p_inode2.directory ∧ p_inode2.nlink = fs[ri[inodekey(p_inode2.ino)]].nlink ∧ p_inode2.nsubdirs = fs[ri[inodekey(p_inode2.ino)]].nsubdirs ∧ p_inode2.size = fs[ri[inodekey(p_inode2.ino)]].size) ∧ p_inode2.ino = old_dent1.ino ∧ (¬ fs[ri[inodekey(old_dent1.ino)]].directory ↔ ¬ fs[ri[inodekey(p_inode1.ino)]].directory) ∧ (fs[ri[inodekey(old_dent1.ino)]].directory → old_dent1.ino ≠ ROOT_INO ∧ dentrykeys(inodekey(old_dent1.ino), ri) = ∅) ∧ p_inode2.ino ≠ ROOT_INO ∧ p_inode2.nlink ≠ 0 ∧ (p_inode2.nlink = 1 → links(p_inode2.ino, fs, ri) = ∅ ++ dentrykey(p_inode0.ino, old_dent1.name)), p_inode.nlink ≠ 0 ∨ p_inode0.ino = ROOT_INO, links(p_inode0.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode0.ino = ROOT_INO, ¬ dentrykey(p_inode0.ino, old_dent1.name) ∈ ri ∧ old_dent1.negdentry? ∨ ( inodekey(old_dent1.ino) ∈ ri ∧ fs[ri[inodekey(old_dent1.ino)]].directory ∨ inodekey(old_dent1.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_dent1.ino)]].directory) ∧ dentrykey(p_inode0.ino, old_dent1.name) ∈ ri ∧ old_dent1.ino = fs[ri[dentrykey(p_inode0.ino, old_dent1.name)]].ino ∧ ( inodekey(p_inode2.ino) ∈ ri ∧ fs[ri[inodekey(p_inode2.ino)]].directory ∧ p_inode2.nlink = fs[ri[inodekey(p_inode2.ino)]].nlink ∧ p_inode2.size = fs[ri[inodekey(p_inode2.ino)]].size ∧ p_inode2.nsubdirs = fs[ri[inodekey(p_inode2.ino)]].nsubdirs ∧ p_inode2.directory ∨ inodekey(p_inode2.ino) ∈ ri ∧ ¬ fs[ri[inodekey(p_inode2.ino)]].directory ∧ p_inode2.nlink = fs[ri[inodekey(p_inode2.ino)]].nlink ∧ p_inode2.nsubdirs = 0 ∧ ¬ p_inode2.directory) ∧ p_inode2.ino = old_dent1.ino ∧ (inodekey(old_dent1.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_dent1.ino)]].directory ↔ ¬ fs[ri[inodekey(p_inode1.ino)]].directory) ∧ (inodekey(old_dent1.ino) ∈ ri ∧ fs[ri[inodekey(old_dent1.ino)]].directory → old_dent1.ino ≠ ROOT_INO ∧ abs-children(old_dent1.ino, fs, ri) = ∅), ¬ fs[ri[inodekey(p_inode1.ino)]].directory ∧ ¬ p_inode1.directory ∧ p_inode1.nlink = fs[ri[inodekey(p_inode1.ino)]].nlink ∧ p_inode1.nsubdirs = fs[ri[inodekey(p_inode1.ino)]].nsubdirs ∨ fs[ri[inodekey(p_inode1.ino)]].directory ∧ p_inode1.directory ∧ p_inode1.nlink = fs[ri[inodekey(p_inode1.ino)]].nlink ∧ p_inode1.nsubdirs = fs[ri[inodekey(p_inode1.ino)]].nsubdirs ∧ p_inode1.size = fs[ri[inodekey(p_inode1.ino)]].size, fs[ri[inodekey(p_inode1.ino)]].directory ∧ p_inode1.nlink = fs[ri[inodekey(p_inode1.ino)]].nlink ∧ p_inode1.size = fs[ri[inodekey(p_inode1.ino)]].size ∧ p_inode1.nsubdirs = fs[ri[inodekey(p_inode1.ino)]].nsubdirs ∧ p_inode1.directory ∨ ¬ fs[ri[inodekey(p_inode1.ino)]].directory ∧ p_inode1.nlink = fs[ri[inodekey(p_inode1.ino)]].nlink ∧ p_inode1.nsubdirs = 0 ∧ ¬ p_inode1.directory ⊦ ⟪aubifs_rename_overwrite_keep_parent# (p_inode1.directory, p_inode1, fi, fo; old_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar3); new_parent_inode := old_parent_inode⟫ ⟨p_inode3 := p_inode1; old_dent0 := mkdentry(str, p_inode1.ino); afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar3) ∧ old_parent_inode = p_inode ∧ new_parent_inode = p_inode0 ∧ p_inode3 = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), p_inode.nlink = 0 ∧ p_inode0.ino ≠ ROOT_INO, ( inodekey(old_dent1.ino) ∈ ri ∧ fs[ri[inodekey(old_dent1.ino)]].directory ∨ inodekey(old_dent1.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_dent1.ino)]].directory) ∧ dentrykey(p_inode0.ino, old_dent1.name) ∈ ri ∧ old_dent1.ino = fs[ri[dentrykey(p_inode0.ino, old_dent1.name)]].ino

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [old_dent1, str0, m]

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ ¬ mkdentry(str, m).negdentry?; (s)%⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: old_dent1, str0, m