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Proof step 144 from proof afs-cons-rename-file-negdentry (previous step)

# entries1 = m1 + 1, files[m] = mkfile(m8, md3, m10, content), dirs0[m] = mkdir(m1 + 1, md2, # links(m, dirs0), # subdirs(m, dirs0), entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m ∈ dirs0, name ∈ entries1, # links(m, dirs0) ≤ 1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files ⊦ entries1 = ∅, name = str, entries1[str] ∈ dirs0, str0 ∈ entries1, (entries1 -- str)[str0, entries1[str]][name] ∈ dirs0, (entries1 -- str)[str0, entries1[str]][name] ∈ files, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: dir-entries name: At-other seq: ⊦ str ≠ str0 → entries[str0, ino][str] = entries[str] subst: [str, str0, entries, ino] → [name, str0, entries1 -- str, entries1[str]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ≠ str0 → (entries -- str0)[str] = entries[str]; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss) Used terms: name, str0, entries1 -- str, entries1[str]