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Proof step 122 from proof inv-rmdir (previous step)

dirs[m] = mkdir(m1, md0, # links(m, dirs), 0, entries0), ROOT_INO ∈ dirs, m ∈ dirs, str ∈ entries0, entries0[str] ∈ dirs, m ∈ dirs ∧ m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → dirs[m].entries = ∅, m ∈ dirs → ¬ m ∈ files ∧ dirs[m].nlink = # links(m, dirs) ∧ dirs[m].nlink ≤ 1 ∧ dirs[m].size = # dirs[m].entries ∧ dirs[m].nsubdirs = # subdirs(m, dirs), m ∈ files → ¬ m ∈ dirs ∧ files[m].nlink = # links(m, dirs), ∀ ino. (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE), ∀ name. m ∈ dirs ∧ name ∈ dirs[m].entries → dirs[m].entries[name] ∈ dirs ∨ dirs[m].entries[name] ∈ files, ∀ n. m ∈ files ∧ n ∈ files[m].content → # files[m].content[n] = VFS_PAGE_SIZE ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 123:
dirs[m] = mkdir(# entries0, md0, # links(m, dirs), 0, entries0), subdirs(m, dirs) = ∅, ROOT_INO ∈ dirs, m ∈ dirs, str ∈ entries0, entries0[str] ∈ dirs, # links(m, dirs) ≤ 1, ∀ ino. (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE), ∀ name. name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files ⊦ entries0 = ∅, m ∈ files, m ≠ ROOT_INO ∧ links(m, dirs) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ # ∅ = 0; (s)%size-zero-02: ⊦ # strings = 0 → strings = ∅; (forward) from specification set-basic[dir-entries]% ⊦ ¬ str ∈ ∅; (s)% ⊦ # ∅ = 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)