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Proof step 30 from proof crash-neutral-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs ⊦ files \ orphans(dirs, files) = files \ (orphans(dirs, files) -- m), m = ROOT_INO

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 32:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs ⊦ m = ROOT_INO, ∀ ino. (ino ∈ files \ orphans(dirs, files) ↔ ino ∈ files \ (orphans(dirs, files) -- m)) ∧ (ino ∈ files \ orphans(dirs, files) → (files \ orphans(dirs, files))[ino] = (files \ (orphans(dirs, files) -- m))[ino])

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files0, files] → [files \ (orphans(dirs, files) -- m), files \ orphans(dirs, files)] flags: <all paths>

Additional information

Used terms: files \ (orphans(dirs, files) -- m), files \ orphans(dirs, files)