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Proof step 18 from proof afs-cons-rename-file-dentry (previous step)

files[dirs[m].entries[str]] = mkfile(m1, md3, # links(dirs[m].entries[str], dirs), content), files[dirs[m0].entries[str0]] = mkfile(m4, md4, m5, content0), new_child_inode = mkinode(dirs[m].entries[str], md, false, # links(dirs[m].entries[str], dirs), 0, m2), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md1, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(dirs[m0].entries[str0], md0, false, m5, 0, m3), old_dent = mkdentry(str0, dirs[m0].entries[str0]), old_parent_inode = mkinode(m0, md2, 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, dirs[m].entries[str] ∈ files, dirs[m0].entries[str0] ∈ files, m = m0 → md1 = md2, 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
files[dirs[m].entries[str]] = mkfile(m1, md3, # links(dirs[m].entries[str], dirs), content), files[dirs[m0].entries[str0]] = mkfile(m4, md4, # links(dirs[m0].entries[str0], dirs), content0), new_child_inode = mkinode(dirs[m].entries[str], md, false, # links(dirs[m].entries[str], dirs), 0, m2), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md1, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(dirs[m0].entries[str0], md0, false, # links(dirs[m0].entries[str0], dirs), 0, m3), old_dent = mkdentry(str0, dirs[m0].entries[str0]), old_parent_inode = mkinode(m0, md2, 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, dirs[m].entries[str] ∈ files, dirs[m0].entries[str0] ∈ files, m = m0 → md1 = md2, 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)

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base