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Proof step 57 from proof crash-neutral-evict (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files ⊦ m = ROOT_INO, m ∈ dirs, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (ino ∈ files ∧ ¬ ino ∈ orphans(dirs, files) → files[ino] = ((files -- m) \ (orphans(dirs, files) -- m))[ino])

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files ∧ ¬ ino ∈ ns → (files \ ns)[ino] = files[ino]; (s)% ⊦ ino ∈ ns -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ ns; (s)% ⊦ ino ∈ files -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ files; (s)% ⊦ ino ∈ files \ ns ↔ ino ∈ files ∧ ¬ ino ∈ ns; (s)