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Proof step 21 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[ino] = mkfile(m0, md, m1, content), dirs[ino] = mkdir(m2, md0, m3, m4, entries), dirs[m] = mkdir(m5, md1, 0, m7, entries0), ROOT_INO ∈ dirs, m ∈ dirs, ino ∈ dirs → m3 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ∀ 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) ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- m) = ∅ → entries = ∅) ∧ ( ino ≠ m ∧ ino ∈ dirs → m3 = # links(ino, dirs -- m) ∧ # links(ino, dirs -- m) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, dirs -- m)) ∧ (ino ∈ files → (ino = m ∨ ¬ ino ∈ dirs) ∧ m1 = # links(ino, dirs -- m)) ∧ (ino ≠ m ∧ ino ∈ dirs ∧ name ∈ entries → entries[name] ≠ m ∧ entries[name] ∈ dirs ∨ entries[name] ∈ files)

User applied rule all left

And obtained the following new goals

Proof step 22:
# links(m, dirs) = 0, dirs[m] = mkdir(m5, md1, 0, m7, entries0), dirs[ino] = mkdir(m2, md0, m3, m4, entries), files[ino] = mkfile(m0, md, m1, content), m ∈ dirs, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files, ino ∈ dirs → m3 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, 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), ∀ name0. m ∈ dirs ∧ name0 ∈ dirs[m].entries → dirs[m].entries[name0] ∈ dirs ∨ dirs[m].entries[name0] ∈ files, ∀ n. m ∈ files ∧ n ∈ files[m].content → # files[m].content[n] = VFS_PAGE_SIZE ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- m) = ∅ → entries = ∅) ∧ ( ino ≠ m ∧ ino ∈ dirs → m3 = # links(ino, dirs -- m) ∧ # links(ino, dirs -- m) ≤ 1 ∧ m2 = # entries ∧ m4 = # subdirs(ino, dirs -- m)) ∧ (ino ∈ files → (ino = m ∨ ¬ ino ∈ dirs) ∧ m1 = # links(ino, dirs -- m)) ∧ (ino ≠ m ∧ ino ∈ dirs ∧ name ∈ entries → entries[name] ≠ m ∧ entries[name] ∈ dirs ∨ entries[name] ∈ files)

Rule argument

pos: left 11 terms: m abort: F discard: T computed: T

Additional information

Used terms: m