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Proof step 32 from proof afs-cons-create-ino (previous step)

dirs[m] = mkdir(# entries0, md3, # links(m, dirs), # subdirs(m, dirs), entries0), files[m] = mkfile(m1, md1, m3, content), (files ++ ino)[m] = mkfile(m4, md2, m5, content0), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, # links(m, dirs) ≤ 1, m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → entries0 = ∅, name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, str ∈ entries0, ino ∈ dirs, ino ∈ files, (m = ROOT_INO ∨ links(m, dirs) ≠ ∅) ∧ (name ∈ entries0[str, ino] → entries0[str, ino][name] ∈ dirs ∨ entries0[str, ino][name] = ino ∨ entries0[str, ino][name] ∈ files)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 33:
(files ++ ino)[m] = mkfile(m4, md2, m5, content0), files[m] = mkfile(m1, md1, m3, content), dirs[m] = mkdir(# entries0, md3, # links(m, dirs), # subdirs(m, dirs), entries0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, # links(m, dirs) ≤ 1, name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → entries0 = ∅, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, name = str, ino ∈ files, ino ∈ dirs, str ∈ entries0, (m = ROOT_INO ∨ links(m, dirs) ≠ ∅) ∧ (name ∈ entries0[str, ino] → entries0[str, ino][name] ∈ dirs ∨ entries0[str, ino][name] = ino ∨ entries0[str, ino][name] ∈ files)

Rule argument

fma: name = str

Additional information

Used simplifier rules: ⊦ str ∈ entries[str0, ino] ↔ str = str0 ∨ str ∈ entries; (ws)% ⊦ entries[str, ino][str] = ino; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s) Used formulas: name = str