+ Definition skolemize_and_flatten_proof :
+ forall {h}{c},
+ ND Rule h c ->
+ ND Rule
+ (mapOptionTree (flatten_judgment ○ skolemize_judgment) h)
+ (mapOptionTree (flatten_judgment ○ skolemize_judgment) c).
+ intros.
+ rewrite mapOptionTree_compose.
+ rewrite mapOptionTree_compose.
+ apply flatten_proof.
+ apply skolemize_proof.
+ apply X.
+ Defined.
+