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Proof step 206 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries0[str], dirs0) = m12 + 1, (ino = m ⊃ (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ;(ino = m0 ⊃ mkdir(m1, md2, # links(m0, dirs0), m2, entries2 -- str0) ;mkdir(# entries4, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries4) ) ) = mkdir(m20, md10, m21, m22, entries5), (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[ino] = mkdir(# entries4, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries4), files[ino] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), dirs0[entries0[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[m] = mkdir(m6, md5, # links(m, dirs0), m9, entries0), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), m0 = m, afs-cons(dirs0, files), ino ∈ dirs0, m ∈ dirs0, str ∈ entries0, entries2[str0] ∈ dirs0, str0 ∈ entries2, m0 ∈ dirs0, entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries4 = ∅, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries0[str] = m0, entries0[str] = m, entries0[str] = ROOT_INO, ino = entries0[str], m22 = # subdirs (ino, dirs0[m0, mkdir(m8, md4, m10, m11, entries[str, 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 ]), m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries2[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 207:
# links(entries2[str], dirs0) = m12 + 1, (ino = m ⊃ mkdir(m8, md1, # links(m, dirs0), m11, (entries2 -- str0)[str, entries2[str0]]) ;mkdir(# entries4, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries4) ) = mkdir(m20, md10, m21, m22, entries5), dirs0[m] = mkdir(m8 + 1, md0, # links(m, dirs0), m11 + 1, entries2), dirs0[entries2[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), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries2[str] ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries2, m ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries4 = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries2[str] = ROOT_INO, entries2[str] = m, ino = entries2[str], m22 = # subdirs(ino, dirs0[m, mkdir(m8, md1, # links(m, dirs0), m11, (entries2 -- str0)[str, entries2[str0]])]), mkdentry(str, entries2[str]) = mkdentry(str0, entries2[str0])

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% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ 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)