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Proof step 6 from proof path-links-empty (previous step)

ispath(p, ino, n, dirs, files) ⊦ # links(n, dirs) = 0 ↔ p = ε ∧ links(ino, dirs) = ∅, p = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
links(n, dirs) = ∅, ispath(p, ino, n, dirs, files), ino ∈ dirs ⊦ p = ε

Rule argument

Additional information

Used simplifier rules: path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs;% ⊦ # ∅ = 0; (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]