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Proof step 318 from proof afs-cons-rename-dir-dentry (previous step)

dirs0[m0] = mkdir(0, md, # links(m0, dirs0), m3, entries2), dirs0[m] = mkdir(m5, md3, # links(m, dirs0), m8, entries0), dirs0[entries0[str]] = mkdir(m2, md5, # links(entries0[str], dirs0), m6, ∅), dirs0[entries2[str0]] = mkdir(m1, md0, # links(entries2[str0], dirs0), m4, entries1), m0 ∈ dirs0, m ∈ dirs0, entries2[str0] ∈ dirs0, entries0[str] ∈ dirs0, str0 ∈ entries2, str ∈ entries0, m = m0 → md1 = md2, ∀ ino. ROOT_INO ∈ dirs0 ∧ (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dir-empty(ino, dirs0, files)) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files ∧ 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)) ∧ (∀ name. ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → valid-ino(dirs0[ino].entries[name], dirs0, files)) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → valid-pagesize(ino, n, files)), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries2[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 319:
dirs0[entries2[str0]] = mkdir(m1, md0, # links(entries2[str0], dirs0), m4, entries1), dirs0[entries0[str]] = mkdir(m2, md5, # links(entries0[str], dirs0), m6, ∅), dirs0[m] = mkdir(m5, md3, # links(m, dirs0), m8, entries0), dirs0[m0] = mkdir(0, md, # links(m0, dirs0), m3, entries2), str ∈ entries0, str0 ∈ entries2, entries0[str] ∈ dirs0, entries2[str0] ∈ dirs0, m ∈ dirs0, m0 ∈ dirs0, ROOT_INO ∈ dirs0, m = m0 → md1 = md2, ∀ ino. (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files ∧ 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)) ∧ (∀ name. ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files) ∧ (∀ n. 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])

Rule argument

Additional information

Used simplifier rules: ⊦ valid-pagesize(ino, n, files) ↔ # files[ino].content[n] = VFS_PAGE_SIZE; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)