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Proof step 26 from proof afs-cons-rename-negdentry (previous step)

dirs[entries0[str]] = mkdir(m9, md5, m11, m12, entries1), dirs[m] = mkdir(m6, md3, # links(m, dirs), m8, entries), files[entries0[str]] = mkfile(m1, md2, # links(entries0[str], dirs), content), dirs[m0] = mkdir(m7, md4, # links(m0, dirs), m10, entries0), new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m8, m6), old_child_inode = mkinode(entries0[str], md1, false, # links(entries0[str], dirs), 0, m4), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m0, md0, true, # links(m0, dirs), m10, m7), afs-cons(dirs, files), entries0[str] ∈ files, m ∈ dirs, m0 ∈ dirs, str ∈ entries0, ¬ str0 ∈ entries, m = m0 → md = md0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: afs-cons-rename-file-negdentry seq: afs-cons(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), valid-file-inode(old_child_inode, dirs, files), old_child_inode.ino = old_dent.ino, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ⊦ ⟪afs_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files ; asynced)⟫ afs-cons(dirs, files) subst: [files, dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, asynced] → [files, dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, asynced] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkdentry(str, m).ino = m; (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)% ⊦ negdentry(str).name = str; (s)% ⊦ negdentry(str).negdentry?; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (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)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (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)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)