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Proof step 125 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]]) ;(ino = m0 ⊃ mkdir(m3, md2, # links(m0, dirs0), m7, 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), afs-cons(dirs0, files0), ino ∈ dirs0, 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 ⊦ # links (ino, dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)] [m, mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ]) = 0, # links (ino, dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)] [m, mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ]) = 1, links (ino, dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)] [m, mkdir(m6, md1, # links(m, dirs0), m10, entries[str, entries1[str0]]) ]) = ∅, m0 = m, mkdentry(str, entries[str]) = mkdentry(str0, entries1[str0]), entries1[str0] ∈ dirs0, entries[str] ∈ dirs0

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: m ∈ dirs0 [m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0) ]

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ p_ino ∈ dirs → links (ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])]) = (ino = ino0 ⊃ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) ++ mklink(p_ino, str) ;(str ∈ entries ∧ entries[str] = ino0 ⊃ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) -- mklink(p_ino, str) ;links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) ) ); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) ∧ ino ≠ ino1 → links(ino0, dirs[ino1, ad][ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs[ino1, ad]); (s)%⊦ ino0 ∈ dirs → links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries -- str)]) = (str ∈ entries ∧ entries[str] = ino ⊃ links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str) ;links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) ); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (s)% ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1); (s) Used formulas: m ∈ dirs0[m0, mkdir(m3, md2, # links(m0, dirs0), m7, entries1 -- str0)]