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Proof step 5 from proof links-add-entry (previous step)

p_ino ∈ dirs ⊦ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino0])]) = links(ino0, 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 6:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 7:
p_ino ∈ dirs ⊦ ∀ alink. alink ∈ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino0])]) ↔ alink ∈ links(ino0, 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(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) ++ mklink(p_ino, str), links (ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino0])])] flags: <all paths>

Additional information

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