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Proof step 50 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 ∈ dirs \ orphans(dirs, files) ↔ ino ∈ dirs \ (orphans(dirs, files) -- m)) ∧ (ino ∈ dirs \ orphans(dirs, files) → (dirs \ orphans(dirs, files))[ino] = (dirs \ (orphans(dirs, files) -- m))[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files, ino ∈ dirs ⊦ dirs[ino] = (dirs \ (orphans(dirs, files) -- m))[ino], m = ROOT_INO, m ∈ dirs, ino ∈ orphans(dirs, files)

Rule argument

Additional information

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