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Proof step 38 from proof inv-recover (previous step)

afs-cons(dirs0, files1) ⊦ afs-cons(dirs0 \ orphans(dirs0, files1), files1 \ orphans(dirs0, files1))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: afs-base name: afs-cons seq: ⊦ afs-cons(dirs, files) ↔ (∀ ino. ROOT_INO ∈ dirs ∧ ( ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty(ino, dirs, files)) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ ( ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino(dirs[ino].entries[name], dirs, files)) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → valid-pagesize(ino, n, files))) subst: [files, dirs] → [files1 \ orphans(dirs0, files1), dirs0 \ orphans(dirs0, files1)] flags: <all paths>

Additional information

Used terms: files1 \ orphans(dirs0, files1), dirs0 \ orphans(dirs0, files1)