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Proof step 157 from proof afs-cons-rename-dir-negdentry (previous step)

# subdirs(m0, dirs0) = m7 + 1, # entries2 = m4 + 1, dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), dirs0[m0] = mkdir(m4 + 1, md, # links(m0, dirs0), m7 + 1, entries2), files[m0] = mkfile(m9, md2, m11, content), afs-cons(dirs0, files), str ∈ entries2, entries2[str] ∈ dirs0, ROOT_INO ∈ dirs0, m0 ∈ dirs0, # links(m0, dirs0) ≤ 1, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m7 + 1 = #((subdirs(m0, dirs0) -- str) ++ str0), entries2 = ∅, str0 ∈ entries2, m0 ≠ ROOT_INO ∧ links(m0, dirs0) = ∅

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 158:
⊦ ¬ str ∈ strings → #(strings ++ str) = # strings + 1
Proof step 159:
# entries2 = m4 + 1, # subdirs(m0, dirs0) = m7 + 1, files[m0] = mkfile(m9, md2, m11, content), dirs0[m0] = mkdir(m4 + 1, md, # links(m0, dirs0), m7 + 1, entries2), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), afs-cons(dirs0, files), m0 ∈ dirs0, ROOT_INO ∈ dirs0, entries2[str] ∈ dirs0, str ∈ entries2, # links(m0, dirs0) ≤ 1, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m7 + 1 = #(subdirs(m0, dirs0) -- str) + 1, entries2 = ∅, str0 ∈ entries2, str0 ∈ subdirs(m0, dirs0) -- str, m0 ≠ ROOT_INO ∧ links(m0, dirs0) = ∅

Rule argument

spec: set-basic, inst: dir-entries name: Size-insert seq: ⊦ ¬ str ∈ strings → #(strings ++ str) = # strings + 1 subst: [str, strings] → [str0, subdirs(m0, dirs0) -- str] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ∈ strings → strings ++ str = strings; (s)% ⊦ 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)% ⊦ ¬ str ∈ entries → entries[str] = (∅)[str]; (s) Used terms: str0, subdirs(m0, dirs0) -- str