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Proof step 45 from proof inv-mkdir (previous step)

dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries0), afs-cons(dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str ∈ entries0, ∃ ino. ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0

Heuristic use patterns applied rule apply lemma

And obtained the following new goals

Proof step 46:
⊦ ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files
Proof step 47:
dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries0), afs-cons(dirs, files), m ∈ dirs, ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str ∈ entries0, ∃ ino. ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0

Rule argument

spec: afs-base name: new-exists seq: ⊦ ∃ ino. ino ≠ 0 ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files subst: [dirs, files] → [dirs, files]

Additional information

Used terms: dirs, files