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Proof step 210 from proof afs-cons-rename-dir-negdentry (previous step)

dirs0[m] = mkdir(m4, md2, # links(m, dirs0), 0, entries), dirs0[m0] = mkdir(m2, md3, # links(m0, dirs0), m5, entries0), dirs0[entries[str]] = mkdir(m1, md, # links(entries[str], dirs0), m3, entries2), ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, str ∈ entries, m ∈ dirs0, m0 ∈ dirs0, 1 ≤ m4, m0 = m → md1 = md0, m ∈ dirs0 ∧ m ≠ ROOT_INO ∧ links(m, dirs0) = ∅ → dirs0[m].entries = ∅, m ∈ dirs0 → ¬ m ∈ files ∧ dirs0[m].nlink = # links(m, dirs0) ∧ dirs0[m].nlink ≤ 1 ∧ dirs0[m].size = # dirs0[m].entries ∧ dirs0[m].nsubdirs = # subdirs(m, dirs0), m ∈ files → ¬ m ∈ dirs0 ∧ files[m].nlink = # links(m, dirs0), ∀ 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), ∀ name. m ∈ dirs0 ∧ name ∈ dirs0[m].entries → dirs0[m].entries[name] ∈ dirs0 ∨ dirs0[m].entries[name] ∈ files, ∀ n. m ∈ files ∧ n ∈ files[m].content → # files[m].content[n] = VFS_PAGE_SIZE, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m4 = 0, str0 ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 211:
dirs0[m] = mkdir(# entries, md2, # links(m, dirs0), 0, entries), dirs0[m0] = mkdir(m2, md3, # links(m0, dirs0), m5, entries0), dirs0[entries[str]] = mkdir(m1, md, # links(entries[str], dirs0), m3, entries2), subdirs(m, dirs0) = ∅, ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, str ∈ entries, m ∈ dirs0, m0 ∈ dirs0, # links(m, dirs0) ≤ # entries, # links(m, dirs0) ≤ 1, 1 ≤ # entries, m0 = m → md1 = md0, ∀ 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), ∀ name. name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries = ∅, m ∈ files, str0 ∈ entries0, m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ # ∅ = 0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ # entries = 0 ↔ entries = ∅; (s)%size-zero-02: ⊦ # strings = 0 → strings = ∅; (forward) from specification set-basic[dir-entries]% ⊦ # ∅ = 0; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat