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Proof step 216 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries[str], dirs0) = m12 + 1, dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), files[ino] = mkfile(m14, md8, m16, content), dirs0[ino] = mkdir(# entries4, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries4), ino = m, mkdir(m8, md1, # links(m, dirs0), m11, entries[str, entries2[str0]]) = mkdir(m20, md10, m21, m22, entries5), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries, m ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries4 = ∅, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] = ROOT_INO, entries[str] = m, entries[str] = m0, ino = entries[str], m0 = m, m22 = # subdirs (ino, dirs0[m0, mkdir(m1, md2, # links(m0, dirs0), m2, entries2 -- str0)] [m, mkdir(m8, md1, # links(m, dirs0), m11, entries[str, entries2[str0]]) ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 217:
# links(entries4[str], dirs0) = m12 + 1, files[m] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), dirs0[entries4[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[m] = mkdir(# entries4, md9, # links(m, dirs0), # subdirs(m, dirs0), entries4), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries4, entries2[str0] ∈ dirs0, str0 ∈ entries2, m0 ∈ dirs0, entries4[str] ∈ dirs0, ROOT_INO ∈ dirs0, # links(m, dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # subdirs(m, dirs0) = #(subdirs(m, dirs0) ++ str), entries4[str] = m0, entries4[str] = m, entries4[str] = ROOT_INO, entries4 = ∅, m0 = m, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ ¬ str ∈ ∅; (s)% ⊦ # ∅ = 0; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → subdirs(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = subdirs(ino0, dirs); (s)%⊦ ino ∈ dirs → subdirs (ino, dirs[ino, mkdir(n, md, n0, n1, entries[str, ino0])]) = (ino0 ∈ dirs ⊃ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) ++ str ;(str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) -- str ;subdirs(ino, dirs[ino, mkdir(n, md, n0, n1, entries)]) ) ); (s)%⊦ subdirs(ino, dirs[ino0, ad0][ino, ad]) = subdirs(ino, dirs[ino, ad]); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)