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Proof step 158 from proof afs-cons-rename-file-dentry (previous step)

# links(entries[str], dirs0) = m11 + 1, (entries1[str0] = entries[str] ⊃ mkfile(m2, md, m11, content1);mkfile(m1, md3, # links(entries1[str0], dirs0), content)) = mkfile(m14, md8, m15, content2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs0[entries1[str0]] = mkdir(m16, md9, m17, m18, entries2), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), afs-cons(dirs0, files0), m ∈ dirs0, entries1[str0] ∈ files0, str0 ∈ entries1, str ∈ entries, m0 ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m0 = m, m15 = #((links(entries1[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str)), entries1[str0] ∈ dirs0, entries[str] ∈ dirs0, mklink(m, str) ∈ links(entries1[str0], dirs0) -- mklink(m0, str0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 159:
# links(entries[str], dirs0) = m11 + 1, files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[entries1[str0]] = mkdir(m16, md9, m17, m18, entries2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries[str] ∈ files0, m0 ∈ dirs0, str ∈ entries, str0 ∈ entries1, entries1[str0] ∈ files0, m ∈ dirs0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # links(entries1[str0], dirs0) = #(links(entries1[str0], dirs0) -- mklink(m0, str0)) + 1, entries1[str0] = entries[str], m0 = m, mklink(m, str) = mklink(m0, str0), entries[str] ∈ dirs0, entries1[str0] ∈ dirs0

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mklink(m, str) = mklink(m0, str0) ↔ m = m0 ∧ str = str0; (ws)% ⊦ 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)