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Proof step 190 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries[str], dirs0) = 1, files[entries[str]] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), dirs0[entries[str]] = mkdir(0, md6, 1, # subdirs(entries[str], dirs0), ∅), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), str ∈ entries, entries2[str0] ∈ dirs0, str0 ∈ entries2, m0 ∈ dirs0, entries[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ #(links(entries[str], dirs0) -- mklink(m, str)) = 0, #(links(entries[str], dirs0) -- mklink(m, str)) = 1, entries2[str0] = entries[str], entries[str] = m0, entries[str] = m, entries[str] = ROOT_INO, links(entries[str], dirs0) = ∅ ++ mklink(m, str), m0 = m

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: lastlink-move: ⊦ # links(entries0[str0], dirs) = 1 ∧ ino0 ∈ dirs ∧ dirs[ino0] = mkdir(m0, md0, n0, n2, entries0) ∧ ino1 ∈ dirs ∧ dirs[ino1] = mkdir(m1, md1, n1, n3, entries1) ∧ str0 ∈ entries0 ∧ str1 ∈ entries1 → (entries0[str0] = entries1[str1] ↔ str0 = str1 ∧ ino0 = ino1);% ⊦ ¬ alink ∈ ls → ls -- alink = ls; (s)% ⊦ alink ∈ ls → #(ls -- alink) = # ls - 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)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s) Used formulas: mklink(m, str) ∈ links(entries[str], dirs0)