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Proof step 46 from proof crash-neutral-evict (previous step)

0 = m1, files[m] = mkfile(m0, md, m1, content), afs-cons(dirs, files), m ∈ files ⊦ m = ROOT_INO, m ∈ dirs, dirs \ orphans(dirs, files) = dirs \ orphans(dirs, files -- m) ∧ files \ orphans(dirs, files) = (files -- m) \ orphans(dirs, files -- m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files ⊦ m = ROOT_INO, m ∈ dirs, dirs \ orphans(dirs, files) = dirs \ (orphans(dirs, files) -- m) ∧ files \ orphans(dirs, files) = (files -- m) \ (orphans(dirs, files) -- m)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ ino ∈ files ∧ files[ino] = mkfile(n, md, 0, content) ∧ afs-cons(dirs, files) → orphans(dirs, files -- ino) = orphans(dirs, files) -- ino; (s)