Theorem zlmplusg

Description: Group operation of a ZZ -module. (Contributed by Mario Carneiro, 2-Oct-2015)

	Ref	Expression
Hypotheses	zlmbas.w	|- W = ( ZMod ` G )
	zlmplusg.2	|- .+ = ( +g ` G )
Assertion	zlmplusg	|- .+ = ( +g ` W )

Proof

Step	Hyp	Ref	Expression
1		zlmbas.w	|- W = ( ZMod ` G )
2		zlmplusg.2	|- .+ = ( +g ` G )
3		df-plusg	|- +g = Slot 2
4		2nn	|- 2 e. NN
5		2lt5	|- 2 < 5
6	1 3 4 5	zlmlem	|- ( +g ` G ) = ( +g ` W )
7	2 6	eqtri	|- .+ = ( +g ` W )