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Proof step 142 from proof afs-cons-rename-dir-negdentry (previous step)

(entries2[str] = m0 ⊃ mkdir(m4 + 1, md1, # links(entries2[str], dirs0), m7 + 1, entries0[str0, entries2[str]]) ;(entries2[str] = m ⊃ mkdir(m1, md0, # links(entries2[str], dirs0), m2, entries2 -- str) ;mkdir(# entries1, md4, # links(entries2[str], dirs0), # subdirs(entries2[str], dirs0), entries1) ) ) = mkdir(m15, md7, m16, m17, entries4), dirs0[entries2[str]] = mkdir(# entries1, md4, # links(entries2[str], dirs0), # subdirs(entries2[str], dirs0), entries1), files[entries2[str]] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), dirs0[m0] = mkdir(m4, md5, # links(m0, dirs0), m7, entries0), afs-cons(dirs0, files), m0 ∈ dirs0, m ∈ dirs0, str ∈ entries2, entries2[str] ∈ dirs0, ROOT_INO ∈ dirs0, # links(entries2[str], dirs0) ≤ 1, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ #(links(entries2[str], dirs0) -- mklink(m, str)) = 0, links(entries2[str], dirs0) = ∅ ++ mklink(m, str), m = m0, str0 ∈ entries0

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 143:
(entries2[str] = m0 ⊃ mkdir(m4 + 1, md1, # links(entries2[str], dirs0), m7 + 1, entries0[str0, entries2[str]]) ;(entries2[str] = m ⊃ mkdir(m1, md0, # links(entries2[str], dirs0), m2, entries2 -- str) ;mkdir(# entries1, md4, # links(entries2[str], dirs0), # subdirs(entries2[str], dirs0), entries1) ) ) = mkdir(m15, md7, m16, m17, entries4), dirs0[m0] = mkdir(m4, md5, # links(m0, dirs0), m7, entries0), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), files[entries2[str]] = mkfile(m9, md2, m11, content), dirs0[entries2[str]] = mkdir(# entries1, md4, # links(entries2[str], dirs0), # subdirs(entries2[str], dirs0), entries1), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries2[str] ∈ dirs0, str ∈ entries2, m ∈ dirs0, m0 ∈ dirs0, mklink(m, str) ∈ links(entries2[str], dirs0), # links(entries2[str], dirs0) ≤ 1, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ #(links(entries2[str], dirs0) -- mklink(m, str)) = 0, links(entries2[str], dirs0) = ∅ ++ mklink(m, str), m = m0, str0 ∈ entries0

Rule argument

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

Additional information

Used simplifier rules: lastlink-rename: ⊦ # links(entries[str0], dirs) = 1 ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(m, md, n, n0, entries) ∧ str0 ∈ entries ∧ str1 ∈ entries → (entries[str0] = entries[str1] ↔ str0 = str1);% ⊦ ¬ alink ∈ ls → ls -- alink = ls; (s)% ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1); (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)%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% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s) Used formulas: mklink(m, str) ∈ links(entries2[str], dirs0)