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Proof step 148 from proof afs-cons-rename-dir-dentry (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 149:
# 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), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries2[str0]] = mkdir(# entries4, md9, # links(entries2[str0], dirs0), # subdirs(entries2[str0], dirs0), entries4), files[entries2[str0]] = mkfile(m14, md8, m16, content), afs-cons(dirs0, files), m ∈ dirs0, ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries, # links(entries2[str0], dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] = ROOT_INO, entries[str] = m, entries[str] = m0, entries2[str0] = entries[str], m0 = m, m21 = #(links(entries2[str0], dirs0) -- mklink(m0, str0)) + 1, mklink(m, str) = mklink(m0, str0)

Rule argument

Additional information

Used simplifier rules: ⊦ mklink(m, str) = mklink(m0, str0) ↔ m = m0 ∧ str = str0; (ws)% ⊦ 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 -- alink0 ↔ alink ≠ alink0 ∧ alink ∈ ls; (s)% ⊦ ¬ alink ∈ ls → #(ls ++ alink) = # ls + 1; (s)