| ⊢ | f ⊃ g ⇒ ⊢ (while w do f) ⊃ (while w do g) | WhileImpWhile | 
Proof:
| 1 | ⊢ f ⊃ g                                          | given                      | 
| 2  | ⊢  (f  ⊃ g)                                            | |
| 3  | ⊢  (f  ⊃ g) ⊃ (while w do f)  ⊃ (while w do g) | |
| 4  | ⊢ (while w do f) ⊃ (while w do g)                   | 
qed