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Proof step 31 from proof inv-renam (previous step)

entries[str0] ∈ files ↔ entries0[str] ∈ files, dirs[entries0[str]] = mkdir(m15, md7, m17, m18, entries1), dirs[m] = mkdir(m12, md5, # links(m, dirs), m14, entries), files[entries0[str]] = mkfile(m5, md3, m9, content), files[entries[str0]] = mkfile(m10, md4, m11, content0), dirs[m4] = mkdir(m13, md6, # links(m4, dirs), m16, entries0), dirs[entries[str0]] = mkdir(m19, md8, m20, m21, entries2), new_child_inode = mkinode(entries[str0], md0, boolvar, m1, m2, m3), new_dent = mkdentry(str0, entries[str0]), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m14, m12), old_child_inode = mkinode(entries0[str], md2, boolvar0, m6, m7, m8), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m4, md1, true, # links(m4, dirs), m16, m13), entries[str0] ≠ ROOT_INO, afs-cons(dirs, files), str0 ∈ entries, m4 ∈ dirs, str ∈ entries0, m ∈ dirs, m = m4 → md = md1, entries[str0] ∈ dirs → entries2 = ∅, entries[str0] ∈ dirs ∧ m1 = m20 ∧ m3 = m19 ∧ m2 = m21 ∧ boolvar ∨ entries0[str] ∈ files ∧ m1 = m11 ∧ m2 = 0 ∧ ¬ boolvar, entries[str0] ∈ dirs ∨ entries0[str] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m4, dirs) ≠ ∅ ∨ m4 = ROOT_INO, entries0[str] ∈ dirs ∨ entries0[str] ∈ files, entries0[str] ∈ dirs ∧ m6 = m17 ∧ m8 = m15 ∧ m7 = m18 ∧ boolvar0 ∨ entries0[str] ∈ files ∧ m6 = m9 ∧ m7 = 0 ∧ ¬ boolvar0 ⊦ ⟪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-dentry 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-wb-inode(old_child_inode, dirs, files), old_child_inode.ino = old_dent.ino, 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, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, 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) ⊦ ⟪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: ⊦ mkdentry(str, m).ino = m; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (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).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (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-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-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (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)