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Proof step 119 from proof afs-cons-rename-file-negdentry (previous step)

(m0 = m ⊃ mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str);mkdir(m7, md5, # links(m0, dirs0), m9, entries2)) = mkdir(m1, md4, m4, m6, entries0), (ino = m0 ⊃ (m0 = m ⊃ mkdir(m1 + 1, md0, m4, m6, entries0[str0, entries1[str]]);mkdir(m1 + 1, md4, m4, m6, entries0[str0, entries1[str]])).meta:= md1 ;(ino = m ⊃ mkdir(m2, md0, # links(m, dirs0), m5, entries1 -- str) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) ) = mkdir(m14, md7, m15, m16, entries3), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m0] = mkdir(m7, md5, # links(m0, dirs0), m9, entries2), files[ino] = mkfile(m8, md3, m10, content), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), afs-cons(dirs0, files), ino ∈ dirs0, ROOT_INO ∈ dirs0, m0 ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m ∈ dirs0, # links(ino, dirs0) ≤ 1, m0 = m → md1 = md0, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino = m, m16 = # subdirs (ino, dirs0 [m, (m = m0 ⊃ mkdir(m1 + 1, md4, m4, m6, entries0[str0, entries1[str]]);mkdir(m2, md2, # links(m, dirs0), m5, entries1 -- str)).meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m1 + 1, md0, m4, m6, entries0[str0, entries1[str]]);mkdir(m1 + 1, md4, m4, m6, entries0[str0, entries1[str]])).meta:= md1 ]), entries1[str] ∈ dirs0, str0 ∈ entries2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 120:
(ino = m0 ⊃ mkdir(m1 + 1, md1, # links(m0, dirs0), m6, entries0[str0, entries1[str]]) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) = mkdir(m14, md7, m15, m16, entries3), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), files[ino] = mkfile(m8, md3, m10, content), dirs0[m0] = mkdir(m1, md5, # links(m0, dirs0), m6, entries0), files[entries1[str]] = mkfile(m3, md, # links(entries1[str], dirs0), content0), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, entries1[str] ∈ files, str ∈ entries1, m0 ∈ dirs0, ROOT_INO ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = m, m0 = m, m16 = # subdirs (ino, dirs0[m, mkdir(m2, md0, # links(m, dirs0), m5, entries1 -- str)] [m0, mkdir(m1 + 1, md1, # links(m0, dirs0), m6, entries0[str0, entries1[str]]) ]), str0 ∈ entries0, entries1[str] ∈ dirs0

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ino0 ≠ ino1 → subdirs(ino0, dirs[ino1, ad]) = subdirs(ino0, dirs); (s)%⊦ p_ino ∈ dirs → subdirs(ino, dirs[p_ino, mkdir(m0 + 1, md, n0, n1, entries)]) = subdirs(ino, dirs[p_ino, mkdir(m0, md, n0, n1, entries)]); (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)