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Proof step 185 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries[str], dirs0) = m12 + 1, (entries2[str0] = m ⊃ mkdir(m8, md1, # links(entries2[str0], dirs0), m11, entries[str, entries2[str0]]) ;(entries2[str0] = m0 ⊃ mkdir(m1, md2, # links(entries2[str0], dirs0), m2, entries2 -- str0) ;mkdir(# entries4, md9, # links(entries2[str0], dirs0), # subdirs(entries2[str0], dirs0), entries4) ) ) = mkdir(m20, md10, m21, m22, entries5), files[entries2[str0]] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(# entries4, md9, # links(entries2[str0], dirs0), # subdirs(entries2[str0], dirs0), entries4), dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), str ∈ entries, entries2[str0] ∈ dirs0, str0 ∈ entries2, m0 ∈ dirs0, entries[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, mklink(m0, str0) ∈ links(entries2[str0], dirs0), # links(entries2[str0], dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ #(links(entries2[str0], dirs0) -- mklink(m0, str0)) = 0, entries2[str0] = entries[str], entries[str] = m0, entries[str] = m, entries[str] = ROOT_INO, links(entries2[str0], dirs0) = ∅ ++ mklink(m0, str0), m0 = m, mklink(m, str) = mklink(m0, str0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 186:
# links(entries[str], dirs0) = m12 + 1, (entries2[str0] = m ⊃ mkdir(m8, md1, # links(entries2[str0], dirs0), m11, entries[str, entries2[str0]]) ;(entries2[str0] = m0 ⊃ mkdir(m1, md2, # links(entries2[str0], dirs0), m2, entries2 -- str0) ;mkdir(# entries4, md9, # links(entries2[str0], dirs0), # subdirs(entries2[str0], dirs0), entries4) ) ) = mkdir(m20, md10, m21, m22, entries5), files[entries2[str0]] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(# entries4, md9, # links(entries2[str0], dirs0), # subdirs(entries2[str0], dirs0), entries4), dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), str ∈ entries, entries2[str0] ∈ dirs0, m0 ∈ dirs0, entries[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, str0 ∈ entries2, # links(entries2[str0], dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links(entries2[str0], dirs0) - 1 = 0, entries2[str0] = entries[str], entries[str] = m0, entries[str] = m, entries[str] = ROOT_INO, links(entries2[str0], dirs0) = ∅ ++ mklink(m0, str0), m0 = m, mklink(m, str) = mklink(m0, str0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mklink(m, str).name = str; (s)% ⊦ mklink(m, str).pino = m; (s)%⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name]; (s)% ⊦ alink ∈ ls → #(ls -- alink) = # ls - 1; (s)