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Proof step 52 from proof inv-link (previous step)

files0[entries[str]] = mkfile(m1, md4, # links(entries[str], dirs0), content0), dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), dirs0[m] = mkdir(# entries1, md5, # links(m, dirs0), # subdirs(m, dirs0), entries1), files0[m] = mkfile(m3, md, m10, content1), dirs0[ino1] = mkdir(m4, md2, # links(ino1, dirs0), m8, entries), entries0[str] = entries[str], afs-cons(dirs0, files0), str ∈ entries, ino1 ∈ dirs0, ino0 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, # links(m, dirs0) ≤ 1, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅ → entries1 = ∅, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m = entries[str], str0 ∈ entries1, (m = ROOT_INO ∨ links(m, dirs0) ≠ ∅) ∧ (name ∈ entries1[str0, entries[str]] → entries1[str0, entries[str]][name] ∈ dirs0 ∨ entries1[str0, entries[str]][name] ∈ files0)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: m = ROOT_INO

Additional information

Used simplifier rules: size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]% ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1); (s)%⊦ str ∈ entries ∧ ¬ str0 ∈ entries → entries[str0, ino][str] = entries[str]; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ str ∈ entries[str0, ino] ↔ str = str0 ∨ str ∈ entries; (ws)% ⊦ str = str0 → entries[str0, ino][str] = ino; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s) Used formulas: m = ROOT_INO