| ⊢ (w ∧ w′) ≡ w ∧ w′ | DfStateAndNextEqv | 
Proof:
| 1 | (w ∧ w′) ⌢ true ≡ w ∧ (w′ ⌢ true) | |
| 2  |  (w ∧ w′) ≡ w ∧ w′        | 1, def. of                | 
| 3  |  w′≡ w′                | |
| 4  | skip ⌢  w′≡skip ⌢ w′        | |
| 5  |   w′≡ w′               | 4, def. of                | 
| 6  |  (w ∧ w′) ≡ w ∧ w′         | 
qed