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Proof step 54 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m7 + 1, files0[entries0[str]] = mkfile(m0, md1, m7 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs0[entries0[str]] = mkdir(m8, md3, m9, m10, entries), afs-cons(dirs0, files0), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m7 = #(links(entries0[str], dirs0) -- mklink(m, str)), entries0[str] ∈ dirs0

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: mklink(m, str) ∈ links(entries0[str], dirs0)

Additional information

Used simplifier rules: ⊦ ¬ 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)% ⊦ m = m + n ↔ n = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ alink ∈ ls → #(ls -- alink) = # ls - 1; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s) Used formulas: mklink(m, str) ∈ links(entries0[str], dirs0)