Theorem rerisefaccl

Description: Closure law for rising factorial. (Contributed by Scott Fenton, 5-Jan-2018)

	Ref	Expression
Assertion	rerisefaccl	|- ( ( A e. RR /\ N e. NN0 ) -> ( A RiseFac N ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		ax-resscn	|- RR C_ CC
2		1re	|- 1 e. RR
3		remulcl	|- ( ( x e. RR /\ y e. RR ) -> ( x x. y ) e. RR )
4		nn0re	|- ( k e. NN0 -> k e. RR )
5		readdcl	|- ( ( A e. RR /\ k e. RR ) -> ( A + k ) e. RR )
6	4 5	sylan2	|- ( ( A e. RR /\ k e. NN0 ) -> ( A + k ) e. RR )
7	1 2 3 6	risefaccllem	|- ( ( A e. RR /\ N e. NN0 ) -> ( A RiseFac N ) e. RR )