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Proof step 36 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m1 + 1, dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)], files = files0[entries0[str], mkfile(m0, md1, m1, content)], afs-cons(dirs0, files0), entries0[str] ∈ files0, str ∈ entries0, m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ afs-cons(dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# links(entries0[str], dirs0) = m1 + 1, files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), afs-cons(dirs0, files0), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, 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 ∈ files0 → ¬ ino ∈ dirs0 ∧ files0[ino].nlink = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files0, ino ∈ files0 ∧ n ∈ files0[ino].content → # files0[ino].content[n] = VFS_PAGE_SIZE, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = ∅ → (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).entries = ∅) ∧ ( ino ∈ dirs0 → (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).nlink = # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ∧ (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).nlink ≤ 1 ∧ (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).size = # (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).entries ∧ (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).nsubdirs = # subdirs(ino, dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)])) ∧ ( ino ∈ files0 → ¬ ino ∈ dirs0 ∧ (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);files0[ino]).nlink = # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0))) ∧ ( ino ∈ dirs0 ∧ name ∈ (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).entries → (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).entries[name] ∈ dirs0 ∨ (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);dirs0[ino]).entries[name] ∈ files0) ∧ ( ino ∈ files0 ∧ n ∈ (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);files0[ino]).content → # (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);files0[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))));% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (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)%⊦ 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)% ⊦ 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)