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Proof step 11 from proof afs-cons-rename-dentry (previous step)

new_child_inode.ino = dirs[m].entries[str], old_child_inode.ino = dirs[m0].entries[str0], new_child_inode.ino ∈ files ↔ old_child_inode.ino ∈ files, new_dent = mkdentry(str, new_child_inode.ino), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_dent = mkdentry(str0, old_child_inode.ino), old_parent_inode = mkinode(m0, md0, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), afs-cons(dirs, files), str ∈ dirs[m].entries, str0 ∈ dirs[m0].entries, m ∈ dirs, m0 ∈ dirs, new_child_inode.ino ∈ dirs → new_child_inode.ino ≠ ROOT_INO ∧ dirs[new_child_inode.ino].entries = ∅, m = m0 → md = md0, new_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, old_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, new_child_inode.ino ∈ dirs ∧ new_child_inode.nlink = dirs[new_child_inode.ino].nlink ∧ new_child_inode.size = dirs[new_child_inode.ino].size ∧ new_child_inode.nsubdirs = dirs[new_child_inode.ino].nsubdirs ∧ new_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ new_child_inode.nlink = files[new_child_inode.ino].nlink ∧ new_child_inode.nsubdirs = 0 ∧ ¬ new_child_inode.directory, old_child_inode.ino ∈ dirs ∧ old_child_inode.nlink = dirs[old_child_inode.ino].nlink ∧ old_child_inode.size = dirs[old_child_inode.ino].size ∧ old_child_inode.nsubdirs = dirs[old_child_inode.ino].nsubdirs ∧ old_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ old_child_inode.nlink = files[old_child_inode.ino].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory ⊦ ⟪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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
old_child_inode.ino = dirs[m0].entries[str0], m1 ∈ files ↔ old_child_inode.ino ∈ files, m1 = dirs[m].entries[str], new_child_inode = mkinode(m1, md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, m1), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_dent = mkdentry(str0, old_child_inode.ino), old_parent_inode = mkinode(m0, md0, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, m = m0 → md = md0, m1 ∈ dirs → m1 ≠ ROOT_INO ∧ dirs[m1].entries = ∅, old_child_inode.ino ∈ dirs ∧ old_child_inode.nlink = dirs[old_child_inode.ino].nlink ∧ old_child_inode.size = dirs[old_child_inode.ino].size ∧ old_child_inode.nsubdirs = dirs[old_child_inode.ino].nsubdirs ∧ old_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ old_child_inode.nlink = files[old_child_inode.ino].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory, m1 ∈ dirs ∧ m2 = dirs[m1].nlink ∧ m4 = dirs[m1].size ∧ m3 = dirs[m1].nsubdirs ∧ boolvar ∨ old_child_inode.ino ∈ files ∧ m2 = files[m1].nlink ∧ m3 = 0 ∧ ¬ boolvar, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, old_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, m1 ∈ dirs ∨ old_child_inode.ino ∈ 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)

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_child_inode, m1, md1, boolvar, m2, m3, m4]

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_child_inode, m1, md1, boolvar, m2, m3, m4