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Proof step 94 from proof afs-cons-rename-dir-negdentry (previous step)

(ino = m0 ⊃ mkdir(m4 + 1, md1, # links(m0, dirs0), m7 + 1, entries0[str0, entries2[str]]) ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) ) = mkdir(m15, md7, m16, m17, entries4), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), dirs0[m0] = mkdir(m4, md5, # links(m0, dirs0), m7, entries0), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), files[ino] = mkfile(m9, md2, m11, content), dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), links (ino, dirs0[m, mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str)] [m0, mkdir(m4 + 1, md1, # links(m0, dirs0), m7 + 1, entries0[str0, entries2[str]]) ]) = ∅, afs-cons(dirs0, files), ino ∈ dirs0, ROOT_INO ∈ dirs0, m0 ∈ dirs0, entries2[str] ∈ dirs0, str ∈ entries2, m ∈ dirs0, m0 ∈ dirs0[m, mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str)], # links(ino, dirs0) ≤ 1, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(ino, dirs0) = ∅ → entries = ∅, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries4 = ∅, ino = ROOT_INO, m0 = m, str0 ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 95:
(ino = m0 ⊃ mkdir(m4 + 1, md1, # links(m0, dirs0), m7 + 1, entries0[str0, entries2[str]]) ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str) ;mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries) ) ) = mkdir(m15, md7, m16, m17, entries4), (entries2[str] = ino ⊃ (links(entries2[str], dirs0) -- mklink(m, str)) ++ mklink(m0, str0);links(ino, dirs0)) = ∅, dirs0[ino] = mkdir(# entries, md6, # links(ino, dirs0), # subdirs(ino, dirs0), entries), files[ino] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), dirs0[m0] = mkdir(m4, md5, # links(m0, dirs0), m7, entries0), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries2, entries2[str] ∈ dirs0, ROOT_INO ∈ dirs0, ino ∈ dirs0, m0 ∈ dirs0, # links(ino, dirs0) ≤ 1, links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries4 = ∅, ino = ROOT_INO, m0 = m, str0 ∈ entries0

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (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) ∧ ino ≠ ino1 → links(ino0, dirs[ino1, ad][ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs[ino1, ad]); (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)%⊦ p_ino ∈ dirs → links(ino, dirs[p_ino, mkdir(m0, md, n0, n1 + 1, entries)]) = links(ino, dirs[p_ino, mkdir(m0, md, n0, n1, entries)]); (s)