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Proof step 126 from proof afs-cons-rename-file-negdentry (previous step)

dirs0[m0] = mkdir(m1 + 1, md2, # links(m0, dirs0), m6, entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[entries1[str]] = mkdir(m11, md6, m12, m13, entries), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m0 ∈ dirs0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links(entries1[str], dirs0) = #((links(entries1[str], dirs0) -- mklink(m0, str)) ++ mklink(m0, str0)), entries1[str] ∈ dirs0, str0 ∈ entries1

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 127:
dirs0[entries1[str]] = mkdir(m11, md6, m12, m13, entries), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m0] = mkdir(m1 + 1, md2, # links(m0, dirs0), m6, entries1), afs-cons(dirs0, files), m0 ∈ dirs0, entries1[str] ∈ files, str ∈ entries1, ROOT_INO ∈ dirs0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links(entries1[str], dirs0) = #((links(entries1[str], dirs0) -- mklink(m0, str)) ++ mklink(m0, str0)), str0 ∈ entries1, entries1[str] ∈ dirs0, mklink(m0, str0) ∈ links(entries1[str], dirs0) -- mklink(m0, str)

Rule argument

fma: mklink(m0, str0) ∈ links(entries1[str], dirs0) -- mklink(m0, 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)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ ¬ str ∈ entries → entries[str] = (∅)[str]; (s) Used formulas: mklink(m0, str0) ∈ links(entries1[str], dirs0) -- mklink(m0, str)