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Proof step 3 from proof links-nonempty (previous step)

dirs[p_ino] = mkdir(m, md, n, n0, entries), links(entries[str], dirs) = ∅, str ∈ entries, p_ino ∈ dirs ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 5:
dirs[p_ino] = mkdir(m, md, n, n0, entries), p_ino ∈ dirs, str ∈ entries, ∀ alink. alink ∈ links(entries[str], dirs) ↔ alink ∈ ∅ ⊦

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [∅, links(entries[str], dirs)] flags: <all paths>

Additional information

Used terms: ∅, links(entries[str], dirs)