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Proof step 86 from proof inv-unlink (previous step)

c_inode.ino = entries[str], c_inode.nlink = files[entries[str]].nlink, c_inode.nsubdirs = 0, dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dent = mkdentry(str, entries[str]), p_ino = p_inode.ino, p_inode = mkinode(m, md, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), pre-unlink(p_inode, c_inode, dent, dirs, files), entries[str] ∈ files, str ∈ entries, m ∈ dirs, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino].size ≥ 1, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ dent.dentry?, c_inode.directory

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)