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Proof step 16 from proof afs-cons-remove-orphans (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 17:
dirs[ino] = mkdir(m1, md0, # links(ino, dirs), m3, entries), files[ino] = mkfile(m, md, m0, content), ROOT_INO ∈ dirs, ino ∈ dirs, 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), ∀ name0. ino ∈ dirs ∧ name0 ∈ dirs[ino].entries → dirs[ino].entries[name0] ∈ dirs ∨ dirs[ino].entries[name0] ∈ files, ∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE ⊦ ino ∈ orphans(dirs, files), (ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅) ∧ # links(ino, dirs) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs) ∧ (name ∈ entries → entries[name] ∈ dirs ∧ ¬ entries[name] ∈ orphans(dirs, files) ∨ entries[name] ∈ files ∧ ¬ entries[name] ∈ orphans(dirs, files))

Rule argument

pos: left 5 terms: ino abort: F discard: T computed: T

Additional information

Used terms: ino