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Proof step 140 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[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, # 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)) ++ mklink(m0, str0)) = 0, #((links(entries2[str], dirs0) -- mklink(m, str)) ++ mklink(m0, str0)) = 1, m = m0, str0 ∈ entries0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 141:
(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)) ++ mklink(m0, str0)) = 1, #((links(entries2[str], dirs0) -- mklink(m, str)) ++ mklink(m0, str0)) = 0, m = m0, str0 ∈ entries0, mklink(m0, str0) ∈ links(entries2[str], dirs0) -- mklink(m, str)

Rule argument

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

Additional information

Used simplifier rules: ⊦ 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)%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ ¬ str ∈ entries → entries[str] = (∅)[str]; (s)% ⊦ ls -- alink = ∅ ↔ ls = ∅ ∨ ls = ∅ ++ alink; (ws)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws) Used formulas: mklink(m0, str0) ∈ links(entries2[str], dirs0) -- mklink(m, str)