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Proof step 95 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(m11, md6, m12, m13, 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(m11, md6, m12, m13, entries), afs-cons(dirs0, files), ino ∈ dirs0, ROOT_INO ∈ dirs0, m0 ∈ dirs0, str ∈ entries1, entries1[str] ∈ files, m ∈ dirs0, ino ∈ dirs0 → m12 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m11 = # entries ∧ m13 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m10 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries1[str] ∈ dirs0, str0 ∈ entries2, m15 = # links (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 ]) ∧ # links (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 ]) ≤ 1 ∧ m14 = # entries3 ∧ 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 ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
(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 ⊦ entries1[str] ∈ dirs0, str0 ∈ entries2, m15 = # links (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 ]) ∧ # links (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 ]) ≤ 1 ∧ m14 = # entries3 ∧ 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 ])

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% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)