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Proof step 14 from proof orphans-del-dir (previous step)

# links(ino, dirs) = 0, files[ino0] = mkfile(m0, md0, m1, content), dirs[ino] = mkdir(n, md, 0, m, ∅), dirs[ino0] = mkdir(m2, md1, m3, m4, entries), afs-cons(dirs, files), ino ∈ dirs, ino0 ∈ dirs → m3 = 0, ino0 ∈ files → m1 = 0, ino0 ≠ ino ∧ ino0 ∈ dirs ∨ ino0 ∈ files ⊦ ino = ROOT_INO, ino0 = ROOT_INO, ino0 ≠ ino ∧ (ino0 ∈ dirs ∨ ino0 ∈ files)

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 3

Additional information

Used simplifier rules: afs-cons-notfile: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files;