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Proof step 264 from proof afs-cons-rename-file-dentry (previous step)

dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries1), files[entries1[str0]] = mkfile(m0, md0, # links(entries1[str0], dirs0), content1), dirs = dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries1)], ino = inode.ino, inode = mkinode(entries1[str0], md, false, # links(entries1[str0], dirs0), 0, m2), afs-cons(dirs0, files), str0 ∈ entries1, entries1[str0] ∈ files, m ∈ dirs0, ino ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ afs-cons(dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]), entries1[str0] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 265:
dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries1), files[entries1[str0]] = mkfile(m0, md0, # links(entries1[str0], dirs0), content1), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files, m ∈ dirs0, ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE, ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ files[ino].nlink = # links(ino, dirs0), 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 ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1[str0] ∈ dirs0, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries = ∅) ∧ ( ino ∈ dirs0 → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nlink = # links(ino, dirs0) ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nlink ≤ 1 ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).size = # (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries ∧ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).nsubdirs = # subdirs(ino, dirs0)) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);files[ino]).nlink = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ name ∈ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries → (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries[name] ∈ dirs0 ∨ (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);dirs0[ino]).entries[name] ∈ files) ∧ ( ino ∈ files ∧ n ∈ (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);files[ino]).content → # (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);files[ino]).content[n] = VFS_PAGE_SIZE)

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))));% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → subdirs(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = subdirs(ino0, dirs); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (s)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ 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)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)