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Proof step 147 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), 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, # 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 ⊦ entries[str] = m0, entries[str] = m, entries[str] = ROOT_INO, m0 = m, m21 = #((links(entries2[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str))

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 148:
# 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)

Rule argument

fma: mklink(m, str) ∈ links(entries2[str0], dirs0) -- mklink(m0, str0)

Additional information

Used simplifier rules: lastlink-move: ⊦ # links(entries0[str0], dirs) = 1 ∧ ino0 ∈ dirs ∧ dirs[ino0] = mkdir(m0, md0, n0, n2, entries0) ∧ ino1 ∈ dirs ∧ dirs[ino1] = mkdir(m1, md1, n1, n3, entries1) ∧ str0 ∈ entries0 ∧ str1 ∈ entries1 → (entries0[str0] = entries1[str1] ↔ str0 = str1 ∧ ino0 = ino1);% ⊦ alink ∈ ls → ls ++ alink = ls; (s)% ⊦ alink ∈ ls -- alink0 ↔ alink ≠ alink0 ∧ alink ∈ ls; (s)%⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name]; (s)% ⊦ mklink(m, str).pino = m; (s)% ⊦ mklink(m, str).name = str; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ # ∅ = 0; (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < 1 ↔ m = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ str ∈ ∅; (s) Used formulas: mklink(m, str) ∈ links(entries2[str0], dirs0) -- mklink(m0, str0)