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Proof step 17 from proof links-add-entry (previous step)

str ∈ entries, p_ino ∈ dirs ⊦ ino = entries[str], links(entries[str], dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])]) = links(entries[str], dirs[p_ino, mkdir(m0, md, n, n0, entries)]) -- mklink(p_ino, str)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 19:
p_ino ∈ dirs, str ∈ entries ⊦ ino = entries[str], ∀ alink. alink ∈ links(entries[str], dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])]) ↔ alink ∈ links(entries[str], dirs[p_ino, mkdir(m0, md, n, n0, entries)]) -- mklink(p_ino, str)

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[p_ino, mkdir(m0, md, n, n0, entries)]) -- mklink(p_ino, str), links (entries[str], dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])])] flags: <all paths>

Additional information

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