| ⊢ | (f ∧fin w) ≡ f ; w | DiAndFinEqvChopState | 
Proof:
| 1 | ⊢ (f ∧fin w) ; true ≡ f ; (w ∧true) | |
| 2  | ⊢ w ∧true ≡ w                      | |
| 3  | ⊢ f ; (w ∧true) ≡ f ; w             | |
| 4  | ⊢ (f ∧fin w) ; true ≡ f ; w          | |
| 5  | ⊢  (f ∧fin w) ≡ f ; w               | 4, def. of                          | 
qed
Here is a corollary of DiAndFinEqvChopState: