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Proof step 135 from proof afs-cons-rename-file-negdentry (previous step)

dirs0[entries1[str]] = mkdir(m11, md6, m12, m13, entries), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), files[entries1[str]] = mkfile(m8, md3, # links(entries1[str], dirs0), content), dirs0[m0] = mkdir(m1, md5, # links(m0, dirs0), m6, entries0), afs-cons(dirs0, files), m0 ∈ dirs0, entries1[str] ∈ files, ROOT_INO ∈ dirs0, str ∈ entries1, m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links(entries1[str], dirs0) = #((links(entries1[str], dirs0) -- mklink(m, str)) ++ mklink(m0, str0)), m = m0, entries1[str] ∈ dirs0, str0 ∈ entries0, mklink(m0, str0) ∈ links(entries1[str], dirs0) -- mklink(m, str)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 136:
dirs0[entries1[str]] = mkdir(m11, md6, m12, m13, entries), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), files[entries1[str]] = mkfile(m8, md3, # links(entries1[str], dirs0), content), dirs0[m0] = mkdir(m1, md5, # links(m0, dirs0), m6, entries0), afs-cons(dirs0, files), m0 ∈ dirs0, entries1[str] ∈ files, ROOT_INO ∈ dirs0, str ∈ entries1, m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links(entries1[str], dirs0) = #(links(entries1[str], dirs0) -- mklink(m, str)) + 1, m = m0, entries1[str] ∈ dirs0, str0 ∈ entries0

Rule argument

Additional information

Used simplifier rules: ⊦ 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)