Description: Closure law for rising factorial. (Contributed by Scott Fenton, 5-Jan-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | nnrisefaccl | |- ( ( A e. NN /\ N e. NN0 ) -> ( A RiseFac N ) e. NN ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnsscn | |- NN C_ CC |
|
2 | 1nn | |- 1 e. NN |
|
3 | nnmulcl | |- ( ( x e. NN /\ y e. NN ) -> ( x x. y ) e. NN ) |
|
4 | nnnn0addcl | |- ( ( A e. NN /\ k e. NN0 ) -> ( A + k ) e. NN ) |
|
5 | 1 2 3 4 | risefaccllem | |- ( ( A e. NN /\ N e. NN0 ) -> ( A RiseFac N ) e. NN ) |