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Proof step 63 from proof inv-rmdir (previous step)

# links(entries0[str], dirs0) = 1, dirs0[entries0[str]] = mkdir(0, md1, 1, # subdirs(entries0[str], dirs0), ∅), files[entries0[str]] = mkfile(m6, md, m8, content), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), afs-cons(dirs0, files), str ∈ entries0, m ∈ dirs0, ROOT_INO ∈ dirs0, entries0[str] ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ 0 = #(links(entries0[str], dirs0) -- mklink(m, str)), entries0[str] = m, entries0[str] = ROOT_INO, links(entries0[str], dirs0) = ∅ ++ mklink(m, str)

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: mklink(m, str) ∈ links(entries0[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);%lastlink-rename: ⊦ # links(entries[str0], dirs) = 1 ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(m, md, n, n0, entries) ∧ str0 ∈ entries ∧ str1 ∈ entries → (entries[str0] = entries[str1] ↔ str0 = str1);% ⊦ ¬ alink ∈ ls → ls -- 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)% ⊦ alink ∈ ls → #(ls -- alink) = # ls - 1; (s) Used formulas: mklink(m, str) ∈ links(entries0[str], dirs0)