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Proof step 3 from proof afs-cons-links-rmorphans (previous step)

afs-cons(dirs, files) ⊦ links(ino, dirs \ orphans(dirs, files)) = links(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:
afs-cons(dirs, files) ⊦ ∀ alink. alink ∈ links(ino, dirs \ orphans(dirs, files)) ↔ alink ∈ links(ino, dirs)

Rule argument

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

Additional information

Used terms: links(ino, dirs), links(ino, dirs \ orphans(dirs, files))