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Proof step 27 from proof links-add-entry (previous step)

p_ino ∈ dirs, ¬ str ∈ entries ∨ entries[str] ≠ ino0 ⊦ ino = ino0, links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])]) = links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 29:
p_ino ∈ dirs, ¬ str ∈ entries ∨ entries[str] ≠ ino0 ⊦ ino = ino0, ∀ alink. alink ∈ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])]) ↔ alink ∈ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)])

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]), links (ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])])] flags: <all paths>

Additional information

Used terms: links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]), links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])])