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Proof step 53 from proof inv-recover (previous step)

dirs0[ino] = mkdir(m1, md0, # links(ino, dirs0), m3, entries), files1[ino] = mkfile(m, md, m0, content), ROOT_INO ∈ dirs0, ino ∈ dirs0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅, ino ∈ dirs0 → ¬ ino ∈ files1 ∧ dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0), ino ∈ files1 → ¬ ino ∈ dirs0 ∧ files1[ino].nlink = # links(ino, dirs0), ∀ ino0. (ino0 ∈ dirs0 ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs0) = ∅ → dirs0[ino0].entries = ∅) ∧ ( ino0 ∈ dirs0 → ¬ ino0 ∈ files1 ∧ dirs0[ino0].nlink = # links(ino0, dirs0) ∧ dirs0[ino0].nlink ≤ 1 ∧ dirs0[ino0].size = # dirs0[ino0].entries ∧ dirs0[ino0].nsubdirs = # subdirs(ino0, dirs0)) ∧ (ino0 ∈ files1 → ¬ ino0 ∈ dirs0 ∧ files1[ino0].nlink = # links(ino0, dirs0)) ∧ (∀ name0. ino0 ∈ dirs0 ∧ name0 ∈ dirs0[ino0].entries → dirs0[ino0].entries[name0] ∈ dirs0 ∨ dirs0[ino0].entries[name0] ∈ files1) ∧ (∀ n. ino0 ∈ files1 ∧ n ∈ files1[ino0].content → # files1[ino0].content[n] = VFS_PAGE_SIZE), ∀ name0. ino ∈ dirs0 ∧ name0 ∈ dirs0[ino].entries → dirs0[ino].entries[name0] ∈ dirs0 ∨ dirs0[ino].entries[name0] ∈ files1, ∀ n. ino ∈ files1 ∧ n ∈ files1[ino].content → # files1[ino].content[n] = VFS_PAGE_SIZE ⊦ ino ∈ orphans(dirs0, files1), (ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅) ∧ # links(ino, dirs0) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs0) ∧ ( name ∈ entries → entries[name] ∈ dirs0 ∧ ¬ entries[name] ∈ orphans(dirs0, files1) ∨ entries[name] ∈ files1 ∧ ¬ entries[name] ∈ orphans(dirs0, files1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
files1[ino] = mkfile(m, md, m0, content), dirs0[ino] = mkdir(# entries, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries), name ∈ entries, ino ∈ dirs0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, ∀ ino0. (ino0 ∈ dirs0 ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs0) = ∅ → dirs0[ino0].entries = ∅) ∧ ( ino0 ∈ dirs0 → ¬ ino0 ∈ files1 ∧ dirs0[ino0].nlink = # links(ino0, dirs0) ∧ dirs0[ino0].nlink ≤ 1 ∧ dirs0[ino0].size = # dirs0[ino0].entries ∧ dirs0[ino0].nsubdirs = # subdirs(ino0, dirs0)) ∧ (ino0 ∈ files1 → ¬ ino0 ∈ dirs0 ∧ files1[ino0].nlink = # links(ino0, dirs0)) ∧ (∀ name0. ino0 ∈ dirs0 ∧ name0 ∈ dirs0[ino0].entries → dirs0[ino0].entries[name0] ∈ dirs0 ∨ dirs0[ino0].entries[name0] ∈ files1) ∧ (∀ n. ino0 ∈ files1 ∧ n ∈ files1[ino0].content → # files1[ino0].content[n] = VFS_PAGE_SIZE), ∀ name0. name0 ∈ entries → entries[name0] ∈ dirs0 ∨ entries[name0] ∈ files1 ⊦ entries = ∅, ino ∈ orphans(dirs0, files1), ino ∈ files1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅, entries[name] ∈ files1 ∧ ¬ entries[name] ∈ orphans(dirs0, files1), entries[name] ∈ dirs0 ∧ ¬ entries[name] ∈ orphans(dirs0, files1)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ 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)