Theorem grpstrndx

Description: A constructed group is a structure. Version not depending on the implementation of the indices. (Contributed by AV, 27-Oct-2024)

	Ref	Expression
Hypothesis	grpfn.g	|- G = { <. ( Base ` ndx ) , B >. , <. ( +g ` ndx ) , .+ >. }
Assertion	grpstrndx	|- G Struct <. ( Base ` ndx ) , ( +g ` ndx ) >.

Proof

Step	Hyp	Ref	Expression
1		grpfn.g	|- G = { <. ( Base ` ndx ) , B >. , <. ( +g ` ndx ) , .+ >. }
2		basendxltplusgndx	|- ( Base ` ndx ) < ( +g ` ndx )
3		plusgndxnn	|- ( +g ` ndx ) e. NN
4	1 2 3	2strstr1	|- G Struct <. ( Base ` ndx ) , ( +g ` ndx ) >.