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Proof step 13 from proof inv-evict (previous step)

0 = dirs[m].nlink, files[ino] = mkfile(m0, md, m1, content), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino ∈ files ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- m) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ≠ m ∧ ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs -- m) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs -- m)) ∧ (ino ∈ files → (ino = m ∨ ¬ ino ∈ dirs) ∧ m1 = # links(ino, dirs -- m)) ∧ (ino ≠ m ∧ ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ≠ m ∧ dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 = dirs[m].nlink, files[ino] = mkfile(m0, md, m1, content), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → 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 ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- m) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ≠ m ∧ ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs -- m) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs -- m)) ∧ (ino ∈ files → (ino = m ∨ ¬ ino ∈ dirs) ∧ m1 = # links(ino, dirs -- m)) ∧ (ino ≠ m ∧ ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ≠ m ∧ dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)