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Proof step 134 from proof afs-cons-rename-file-dentry (previous step)

# links(entries0[str], dirs0) = m11 + 1, (ino = m ⊃ (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 ;(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), (m = m0 ⊃ mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0);mkdir(m4, md6, # links(m, dirs0), m8, entries0)) = mkdir(m6, md5, m9, m10, entries), dirs0[ino] = mkdir(# entries2, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries2), dirs0[m0] = mkdir(m3 + 1, md4, # links(m0, dirs0), m7, entries1), files0[entries1[str0]] = mkfile(m1, md3, # links(entries1[str0], dirs0), content), files0[entries0[str]] = mkfile(m5, md0, m11 + 1, content1), dirs0[m] = mkdir(m4, md6, # links(m, dirs0), m8, entries0), files0[ino] = mkfile(m12, md7, m13, content0), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries0[str] ∈ files0, m0 ∈ dirs0, str ∈ entries0, entries1[str0] ∈ files0, str0 ∈ entries1, m ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m21 = # subdirs (ino, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md5, m9, m10, entries[str, entries1[str0]]);mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 ]), entries0[str] ∈ dirs0, entries1[str0] ∈ dirs0, m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 135:
# links(entries0[str], dirs0) = m11 + 1, (m = m0 ⊃ mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0);mkdir(m4, md6, # links(m, dirs0), m8, entries0)) = mkdir(m6, md5, m9, m10, entries), (ino = m ⊃ (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 ;(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(m4, md6, # links(m, dirs0), m8, entries0), files0[entries0[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 ∈ entries0, m0 ∈ dirs0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, m = m0 → md1 = md2, 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, m21 = # subdirs (ino, dirs0 [m0, (m0 = m ⊃ mkdir(m6, md5, m9, m10, entries[str, entries1[str0]]);mkdir(m3, md4, # links(m0, dirs0), m7, entries1 -- str0)).meta:= md2 ] [m, (m = m0 ⊃ mkdir(m6, md2, m9, m10, entries[str, entries1[str0]]);mkdir(m6, md5, m9, m10, entries[str, entries1[str0]])).meta:= md1 ]), entries1[str0] ∈ dirs0, entries0[str] ∈ dirs0, m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries1[str0])

Rule argument

fma: ino = m0

Additional information

Used simplifier rules: ⊦ 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)% ⊦ # ∅ = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ino0 ≠ ino1 → subdirs(ino0, dirs[ino1, ad]) = subdirs(ino0, dirs); (s)%⊦ ino ∈ 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)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → subdirs(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = subdirs(ino0, dirs); (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (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)% ⊦ str ∈ entries -- str0 ↔ str ≠ str0 ∧ str ∈ entries; (s)% ⊦ str ≠ str0 → (entries -- str0)[str] = entries[str]; (s) Used formulas: ino = m0