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

dirs[ino] = mkdir(m0, md0, n1, n2, entries), ino ∈ dirs ⊦ links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, 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[ino] = mkdir(m0, md0, n1, n2, entries), ino ∈ dirs ⊦ ∀ alink. alink ∈ links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) ↔ alink ∈ links(ino0, dirs)

Rule argument

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

Additional information

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