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Proof step 209 from proof afs-cons-rename-dir-dentry (previous step)

# subdirs(m, dirs0) = m22 + 1, # entries2 = m8 + 1, # links(entries2[str], dirs0) = m12 + 1, dirs0[entries2[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), files[m] = mkfile(m14, md8, m16, content), dirs0[m] = mkdir(m8 + 1, md0, # links(m, dirs0), m22 + 1, entries2), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries2[str] ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries2, m ∈ dirs0, # links(m, dirs0) ≤ 1, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries2[str] = ROOT_INO, entries2[str] = m, entries2 = ∅, m22 = #((subdirs(m, dirs0) -- str0) ++ str), mkdentry(str, entries2[str]) = mkdentry(str0, entries2[str0]), m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-basic, inst: dir-entries name: Size-insert seq: ⊦ ¬ str ∈ strings → #(strings ++ str) = # strings + 1 subst: [str, strings] → [str, subdirs(m, dirs0) -- str0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ∈ strings -- str0 ↔ str ≠ str0 ∧ str ∈ strings; (s)%⊦ str ∈ subdirs(ino, dirs) ↔ ino ∈ dirs ∧ str ∈ dirs[ino].entries ∧ dirs[ino].entries[str] ∈ dirs; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s) Used terms: str, subdirs(m, dirs0) -- str0