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Proof step 100 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), 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), dirs = dirs0[entries0[str], mkdir(m13, md7, m12, m15, entries3)] [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 ], ino = inode.ino, inode = mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m5, m3), afs-cons(dirs0, files), ino ∈ dirs, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, entries0[str] ∈ dirs0, str ∈ entries0, m ∈ dirs0, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files), ino ∈ files, m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries2[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 101:
(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] = 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), 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) = ∅ → dirs0[ino].entries = ∅, ino ∈ dirs0 → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0), ino ∈ files → ¬ ino ∈ dirs0 ∧ files[ino].nlink = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files, ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ 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 ⊃ (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 = 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);dirs0[ino]) ) ) .entries = ∅) ∧ ( ino ∈ dirs0 → (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);dirs0[ino]) ) ) .nlink = # 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 = 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);dirs0[ino]) ) ) .nlink ≤ 1 ∧ (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);dirs0[ino]) ) ) .size = # (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);dirs0[ino]) ) ) .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);dirs0[ino]) ) ) .nsubdirs = # 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 ∧ files[ino].nlink = # 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 ∈ (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);dirs0[ino]) ) ) .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);dirs0[ino]) ) ) .entries [name ] ∈ dirs0 ∨ (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);dirs0[ino]) ) ) .entries [name ] ∈ files)

Rule argument

Additional information

Used simplifier rules: afs-cons-reduce: ⊦ afs-cons(dirs0, files0) → ( afs-cons(dirs1, files1) ↔ (∀ ino, name, n. ROOT_INO ∈ dirs0 ∧ ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dir-empty(ino, dirs0, files0)) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files0 ∧ dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ ( ino ∈ files0 → ¬ ino ∈ dirs0 ∧ files0[ino].nlink = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → valid-ino(dirs0[ino].entries[name], dirs0, files0)) ∧ ( ino ∈ files0 ∧ n ∈ files0[ino].content → valid-pagesize(ino, n, files0)) → ROOT_INO ∈ dirs1 ∧ ( ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → dir-empty(ino, dirs1, files1)) ∧ ( ino ∈ dirs1 → ¬ ino ∈ files1 ∧ dirs1[ino].nlink = # links(ino, dirs1) ∧ dirs1[ino].nlink ≤ 1 ∧ dirs1[ino].size = # dirs1[ino].entries ∧ dirs1[ino].nsubdirs = # subdirs(ino, dirs1)) ∧ ( ino ∈ files1 → ¬ ino ∈ dirs1 ∧ files1[ino].nlink = # links(ino, dirs1)) ∧ ( ino ∈ dirs1 ∧ name ∈ dirs1[ino].entries → valid-ino(dirs1[ino].entries[name], dirs1, files1)) ∧ ( ino ∈ files1 ∧ n ∈ files1[ino].content → valid-pagesize(ino, n, files1))));% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)%⊦ valid-pagesize(ino, n, files) ↔ # files[ino].content[n] = VFS_PAGE_SIZE; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)%⊦ dirs[ino, ad][ino0, ad0][ino1, ad1][ino, ad2] = dirs[ino0, ad0][ino1, ad1][ino, ad2]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)