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Proof step 3 from proof subdirs-delete-orphans (previous step)

⊦ subdirs(ino, dirs \ orphans(dirs, files)) = subdirs(ino, dirs), ino ∈ orphans(dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ strings = strings0 ↔ (∀ str. str ∈ strings ↔ str ∈ strings0)
Proof step 5:
⊦ ino ∈ orphans(dirs, files), ∀ str. str ∈ subdirs(ino, dirs \ orphans(dirs, files)) ↔ str ∈ subdirs(ino, dirs)

Rule argument

spec: set-basic, inst: dir-entries name: Extension seq: ⊦ strings = strings0 ↔ (∀ str. str ∈ strings ↔ str ∈ strings0) subst: [strings0, strings] → [subdirs(ino, dirs), subdirs(ino, dirs \ orphans(dirs, files))] flags: <all paths>

Additional information

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