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Proof step 140 from proof afs-cons-rename-file-negdentry (previous step)

(ino = m ⊃ mkdir(m1 + 1, md1, # links(m, dirs0), m6, (entries1 -- str)[str0, entries1[str]]) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) = mkdir(m14, md7, m15, m16, entries3), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(m1 + 1, md2, # links(m, dirs0), m6, entries1), files[ino] = mkfile(m8, md3, m10, content), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), afs-cons(dirs0, files), ino ∈ dirs0, name ∈ entries3, ROOT_INO ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1[str] ∈ dirs0, str0 ∈ entries1, entries3[name] ∈ dirs0, entries3[name] ∈ files

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 141:
(ino = m ⊃ mkdir(m1 + 1, md1, # links(m, dirs0), m6, (entries1 -- str)[str0, entries1[str]]) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) = mkdir(m14, md7, m15, m16, entries3), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), files[ino] = mkfile(m8, md3, m10, content), dirs0[m] = mkdir(m1 + 1, md2, # links(m, dirs0), m6, entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), ino = m, afs-cons(dirs0, files), m ∈ dirs0, entries1[str] ∈ files, str ∈ entries1, ROOT_INO ∈ dirs0, name ∈ entries3, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries3[name] ∈ files, entries3[name] ∈ dirs0, str0 ∈ entries1, entries1[str] ∈ dirs0

Rule argument

fma: ino = m

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss) Used formulas: ino = m