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Proof step 173 from proof afs-cons-rename-file-dentry (previous step)

# links(entries[str], dirs0) = m11 + 1, (ino = m ⊃ mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ;mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2) ) = mkdir(m19, md10, m20, m21, entries3), files0[ino] = mkfile(m12, md7, m13, content0), dirs0[m] = mkdir(m6, md6, # links(m, dirs0), m10, entries), files0[entries[str]] = mkfile(m5, md0, m11 + 1, content1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), dirs0[ino] = mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2), ino = m, afs-cons(dirs0, files0), ino ∈ dirs0, name ∈ entries3, m ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files0, str ∈ entries, m0 ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino = m0, m = m0, entries1[str0] ∈ dirs0, entries[str] ∈ dirs0, entries3[name] ∈ dirs0, entries3[name] ∈ files0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 174:
# links(entries2[str], dirs0) = m11 + 1, dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), files0[entries2[str]] = mkfile(m5, md0, m11 + 1, content1), dirs0[m] = mkdir(# entries2, md9, # links(m, dirs0), # subdirs(m, dirs0), entries2), files0[m] = mkfile(m12, md7, m13, content0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries2[str] ∈ files0, m0 ∈ dirs0, str ∈ entries2, entries1[str0] ∈ files0, str0 ∈ entries1, name ∈ entries2[str, entries1[str0]], m ∈ dirs0, name ∈ entries2, # links(m, dirs0) ≤ 1, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0 ⊦ entries2 = ∅, m = m0, entries2[str, entries1[str0]][name] ∈ files0, entries2[str, entries1[str0]][name] ∈ dirs0, entries2[str] ∈ dirs0, entries1[str0] ∈ dirs0, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ ¬ str ∈ ∅; (s)% ⊦ # ∅ = 0; (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 = str0 → entries[str0, ino][str] = ino; (s)% ⊦ str ∈ entries[str0, ino] ↔ str = str0 ∨ str ∈ entries; (ws)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)