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Proof step 20 from proof refine-renam (previous step)

⟨afs_rename#(; old_parent_inode0, new_parent_inode0, old_child_inode, new_child_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( (dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (boolvar → boolvar4)) ∧ old_parent_inode1 = old_parent_inode0 ∧ new_parent_inode1 = new_parent_inode0 ∧ p_inode1 = old_child_inode ∧ p_inode2 = new_child_inode ∧ old_dent2 = old_dent0 ∧ new_dent0 = old_dent1 ∧ err1 = err0), ⟨aubifs_rename_new_reparent# (p_inode1.directory, p_inode1, fi, ro, fo; old_parent_inode, new_parent_inode, old_dent, new_dent, err, ri, fs, log, boolvar3)⟩ ( old_parent_inode = old_parent_inode1 ∧ new_parent_inode = new_parent_inode1 ∧ old_dent = old_dent2 ∧ new_dent = new_dent0 ∧ err = err1 ∧ ri = ri0 ∧ fs = fs0 ∧ log = log0 ∧ (boolvar3 ↔ boolvar4)), ⟪aubifs_rename_new_reparent# (p_inode1.directory, p_inode1, fi, ro, fo; old_parent_inode, new_parent_inode, old_dent, new_dent, err, ri, fs, log, boolvar3)⟫ ⟨afs_rename#(; old_parent_inode0, new_parent_inode0, old_child_inode, new_child_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( (dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (boolvar → boolvar3)) ∧ old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ p_inode1 = old_child_inode ∧ p_inode2 = new_child_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), boolvar2 ↔ boolvar3, boolvar1 ↔ new_dent.dentry?, boolvar0 ↔ old_parent_inode.ino ≠ new_parent_inode.ino, boolvar ↔ old_child_inode.directory, boolvar0, ¬ boolvar1, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = p_inode2, new_dent = old_dent1, new_parent_inode = p_inode0, new_parent_inode0 = new_parent_inode, old_child_inode = p_inode1, old_dent = old_dent0, old_parent_inode = p_inode, old_parent_inode0 = old_parent_inode, orphans(dirs, files) = abs-keys(ro), fo.inodes?, ro.inodes?, afs-cons(dirs, files), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, fs, ri, ro), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), asynced → boolvar3 ⊦ ⟨afs_rename#(; p_inode, p_inode0, p_inode1, p_inode2, old_dent0, old_dent1, err0, dirs, files; asynced)⟩ ( (dirs = abs-dirs(fs0, ri0) ∧ files = abs-files(fs0, ri0) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (asynced → boolvar4)) ∧ old_parent_inode1 = p_inode ∧ new_parent_inode1 = p_inode0 ∧ old_child_inode = p_inode1 ∧ new_child_inode = p_inode2 ∧ old_dent2 = old_dent0 ∧ new_dent0 = old_dent1 ∧ err1 = err0)

User applied rule execute call

And closed the goal!

Rule argument

poslist: left 1, right 1

Additional information

Used simplifier rules: ⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)%⊦ ro.inodes? → (abs-keys(ro) = abs-keys(orphans(fs, ri)) ↔ ro = orphans(fs, ri)); (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, fs, ri, ro) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, fs, ri, ro) ∨ valid-dentry(new_parent_inode.ino, new_dent, fs, ri, ro) ∧ valid-wb-inode(new_child_inode, fs, ri) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, fs, ri) ↔ valid-file-ino(old_dent.ino, fs, ri)) ∧ ( valid-dir-ino(new_dent.ino, fs, ri) → new_dent.ino ≠ ROOT_INO ∧ dentrykeys(inodekey(new_dent.ino), ri) = ∅) ∧ new_child_inode.ino ≠ ROOT_INO ∧ new_child_inode.nlink ≠ 0 ∧ ( new_child_inode.nlink = 1 → links(new_child_inode.ino, fs, ri) = {dentrykey(new_parent_inode.ino, new_dent.name)} )) ∧ valid-dentry(old_parent_inode.ino, old_dent, fs, ri, ro) ∧ valid-dir-inode(new_parent_inode, fs, ri) ∧ valid-dir-inode(old_parent_inode, fs, ri) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, fs, ri) ∧ old_child_inode.ino = old_dent.ino ∧ old_parent_inode.size ≥ 1 ∧ (old_child_inode.directory → old_parent_inode.nsubdirs ≥ 1); (s)%⊦ valid-negdentry(ino, dent, fs, ri, ro) ↔ dent.negdentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ ¬ dentrykey(ino, dent.name) ∈ ri; (s)%⊦ valid-parent-ino(ino, fs, ri, ro) ↔ ( valid-dir-ino(ino, fs, ri) ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO)) ∧ ¬ inodekey(ino) ∈ ro; (s)%⊦ valid-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-dentry(ino, dent, fs, ri, ro) ↔ dent.dentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ valid-ino(dent.ino, fs, ri) ∧ dentrykey(ino, dent.name) ∈ ri ∧ fs[ri[dentrykey(ino, dent.name)]].ino = dent.ino; (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)%⊦ valid-dir-inode(inode, fs, ri) ↔ valid-dir-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs ∧ inode.size = fs[ri[inodekey(inode.ino)]].size; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ valid-wb-inode(inode, fs, ri) ↔ valid-file-inode(inode, fs, ri) ∨ valid-dir-inode(inode, fs, ri); (s)%⊦ valid-file-inode(inode, fs, ri) ↔ valid-file-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs; (s)%⊦ valid-file-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)