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Proof step 62 from proof crash-neutral-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files, ino ∈ files ⊦ m = ROOT_INO, m ∈ dirs, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (¬ ino ∈ orphans(dirs, files) → files[ino] = ((files \ (orphans(dirs, files) -- m)) -- m)[ino])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
ino ∈ files ⊦ ino ≠ ino0 → (files -- ino0)[ino] = files[ino]
Proof step 64:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), ino ∈ files, m ∈ files ⊦ m = ROOT_INO, m ∈ dirs, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (¬ ino ∈ orphans(dirs, files) → files[ino] = ((files \ (orphans(dirs, files) -- m)) -- m)[ino]), ino ∈ files \ (orphans(dirs, files) -- m) ∧ ino ≠ m
Proof step 69:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), ino ∈ files, m ∈ files, ino ∈ files \ (orphans(dirs, files) -- m) ⊦ ino = m, m = ROOT_INO, m ∈ dirs, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (¬ ino ∈ orphans(dirs, files) → files[ino] = (files \ (orphans(dirs, files) -- m))[ino])

Rule argument

spec: heap, inst: file-heap name: at-del seq: ino ∈ files ⊦ ino ≠ ino0 → (files -- ino0)[ino] = files[ino] subst: [ino, ino0, files] → [ino, m, files \ (orphans(dirs, files) -- m)] flags: <all paths>

Additional information

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