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Proof step 108 from proof afs-cons-rename-dir-dentry (previous step)

(entries0[str] = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]) ;(entries0[str] = m0 ⊃ mkdir(m1, md0, # links(entries0[str], dirs0), m2, entries2 -- str0) ;mkdir(m3, md6, # links(entries0[str], dirs0), m5, ∅) ) ) = mkdir(m13, md7, m12 + 1, m15, entries3), (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0);mkdir(m6, md5, # links(m, dirs0), m9, entries0)) = mkdir(m8, md4, m10, m11, entries), (ino = entries0[str] ⊃ (entries0[str] = m ⊃ (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ;(ino = m ⊃ (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ;(ino = m0 ⊃ mkdir(m1, md2, # links(m0, dirs0), m2, entries2 -- str0);mkdir(m17, md9, m18, m19, entries4)) ) ) = mkdir(m20, md10, m21, m22, entries5), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), dirs0[m] = mkdir(m6, md5, # links(m, dirs0), m9, entries0), dirs0[entries0[str]] = mkdir(m3, md6, # links(entries0[str], dirs0), m5, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), files[ino] = mkfile(m14, md8, m16, content), dirs0[ino] = mkdir(m17, md9, m18, m19, entries4), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries0[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries0, m ∈ dirs0, ino ∈ dirs0 → m18 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m17 = # entries4 ∧ m19 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m16 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries4 = ∅, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m, ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md2 ;(m = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])) ) .meta:= md1 ] [entries0[str], (entries0[str] = m ⊃ (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ]) = ∅ → entries5 = ∅) ∧ ( ino ∈ dirs0 → m21 = # links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md2 ;(m = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])) ) .meta:= md1 ] [entries0[str], (entries0[str] = m ⊃ (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ]) ∧ # links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md2 ;(m = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])) ) .meta:= md1 ] [entries0[str], (entries0[str] = m ⊃ (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ]) ≤ 1 ∧ m20 = # entries5 ∧ m22 = # subdirs (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md2 ;(m = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])) ) .meta:= md1 ] [entries0[str], (entries0[str] = m ⊃ (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ])) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ m16 = # links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md2 ;(m = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])) ) .meta:= md1 ] [entries0[str], (entries0[str] = m ⊃ (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ])) ∧ (ino ∈ dirs0 ∧ name ∈ entries5 → entries5[name] ∈ dirs0 ∨ entries5[name] ∈ files), m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries2[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 109:
(ino = entries0[str] ⊃ (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md ;(ino = m ⊃ (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ;(ino = m0 ⊃ mkdir(m1, md2, # links(m0, dirs0), m2, entries2 -- str0);mkdir(m17, md9, m18, m19, entries4)) ) ) = mkdir(m20, md10, m21, m22, entries5), (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0);mkdir(m6, md5, # links(m, dirs0), m9, entries0)) = mkdir(m8, md4, m10, m11, entries), (entries0[str] = m0 ⊃ mkdir(m1, md0, # links(entries0[str], dirs0), m2, entries2 -- str0) ;mkdir(m3, md6, # links(entries0[str], dirs0), m5, ∅) ) = mkdir(m13, md7, m12 + 1, m15, entries3), dirs0[ino] = mkdir(m17, md9, m18, m19, entries4), files[ino] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), dirs0[entries0[str]] = mkdir(m3, md6, # links(entries0[str], dirs0), m5, ∅), dirs0[m] = mkdir(m6, md5, # links(m, dirs0), m9, entries0), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries0, entries2[str0] ∈ dirs0, str0 ∈ entries2, m0 ∈ dirs0, entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, m = m0 → md1 = md2, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries4 = ∅, ino ∈ files → ¬ ino ∈ dirs0 ∧ m16 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, ino ∈ dirs0 → m18 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m17 = # entries4 ∧ m19 = # subdirs(ino, dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries0[str] = m, entries0[str] = ROOT_INO, m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries2[str0]), ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ] [entries0[str], (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md ]) = ∅ → entries5 = ∅) ∧ ( ino ∈ dirs0 → m21 = # links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ] [entries0[str], (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md ]) ∧ # links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ] [entries0[str], (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md ]) ≤ 1 ∧ m20 = # entries5 ∧ m22 = # subdirs (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ] [entries0[str], (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md ])) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ m16 = # links (ino, dirs0 [m0, (m0 = entries0[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md4, m10, m11, entries[str, entries2[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ mkdir(m8, md2, m10, m11, entries[str, entries2[str0]]);mkdir(m8, md4, m10, m11, entries[str, entries2[str0]])).meta:= md1 ] [entries0[str], (entries0[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md ])) ∧ (ino ∈ dirs0 ∧ name ∈ entries5 → entries5[name] ∈ dirs0 ∨ entries5[name] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)