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Proof step 2 from proof inv-link (previous step)

afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache) ⊦ ⟪cache_link#(old_dent; p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
c_inode.ino = old_dent.ino, old_dent.ino = dirs[ino].entries[old_dent.name], c_inode.nlink = files[old_dent.ino].nlink, p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nsubdirs = 0, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, p_inode.size = dirs[p_inode.ino].size, old_dent.dentry?, p_inode.directory, new_dent.negdentry?, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), old_dent.ino ∈ files, p_inode.ino ∈ dirs, old_dent.name ∈ dirs[ino].entries, ino ∈ dirs, ¬ c_inode.directory, ¬ new_dent.name ∈ dirs[p_inode.ino].entries, asynced → synced(files, icache, pcache), links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪cache_link#(old_dent; p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ 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-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (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-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (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-dentry(dent, dirs, files) ↔ (∃ ino. valid-dentry(ino, dent, dirs, files)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ↔ valid-dentry(old_dent, dirs, files) ∧ valid-negdentry(p_inode.ino, new_dent, dirs, files) ∧ (links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO) ∧ valid-dir-inode(p_inode, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ c_inode.ino = old_dent.ino; (s)