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Proof step 51 from proof inv-mkdir (previous step)

dirs[ino0] = mkdir(m, md0, # links(ino0, dirs), m1, entries), dent = negdentry(str), err = EEXISTS, err0 = ESUCCESS, err1 = ESUCCESS, p_ino = ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pre-lookup(p_ino, dent, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, dent.name ∈ dirs[p_ino].entries ⊦ ⟪skip⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Heuristic symbolic execution applied rule skip right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ negdentry(str).name = str; (s)%⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)