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Proof step 228 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries0[str], dirs0) = m12 + 1, (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0);mkdir(m6, md5, # links(m, dirs0), m9, entries0)) = mkdir(m8, md4, m10, m11, entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), dirs0[m] = mkdir(m6, md5, # links(m, dirs0), m9, entries0), dirs0[entries0[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), files[ino] = mkfile(m14, md8, # links(ino, dirs0), content), dirs0[ino] = mkdir(m17, md9, m18, m19, entries4), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries0[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries0, m ∈ dirs0, ino ∈ files, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # links(ino, dirs0) = # links (ino, dirs0[m0, mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0).meta:= md2] [m, (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ]), entries0[str] = ROOT_INO, entries0[str] = m, entries0[str] = m0, m0 = m, mkdentry(str, entries0[str]) = mkdentry(str0, entries2[str0]), ino ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 229:
# 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, # links(ino, dirs0), content), dirs0[ino] = mkdir(m17, md9, m18, m19, entries4), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries, m ∈ dirs0, ino ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # links(ino, dirs0) = # links (ino, dirs0[m0, mkdir(m1, md2, # links(m0, dirs0), m2, entries2 -- str0)] [m, mkdir(m8, md1, # links(m, dirs0), m11, entries[str, entries2[str0]]) ]), entries[str] = ROOT_INO, entries[str] = m, entries[str] = m0, m0 = m, mkdentry(str, entries[str]) = mkdentry(str0, entries2[str0]), ino ∈ 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%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)