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

afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-unlink(p_inode, c_inode, dent, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache) ⊦ ⟪cache_unlink#(; p_inode, c_inode, 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 = dent.ino, dent.ino = dirs[p_inode.ino].entries[dent.name], p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nlink = files[dent.ino].nlink, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, c_inode.nsubdirs = 0, p_inode.size = dirs[p_inode.ino].size, dent.dentry?, p_inode.directory, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), dent.ino ∈ files, dent.name ∈ dirs[p_inode.ino].entries, p_inode.ino ∈ dirs, ¬ c_inode.directory, asynced → synced(files, icache, pcache), links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ ⟪cache_unlink#(; p_inode, c_inode, 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-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-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-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)%⊦ pre-unlink(p_inode, c_inode, dent, dirs, files) ↔ valid-dentry(p_inode.ino, dent, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ valid-dir-inode(p_inode, dirs, files) ∧ c_inode.ino = dent.ino; (s)