Theorem basendxltplusgndx

Description: The index of the slot for the base set is less then the index of the slot for the group operation in an extensible structure. (Contributed by AV, 17-Oct-2024)

	Ref	Expression
Assertion	basendxltplusgndx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<{+}_{\mathrm{ndx}}$$

Proof

Step	Hyp	Ref	Expression
1		1lt2	$$⊢1<2$$
2		basendx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}=1$$
3		plusgndx	$$⊢{+}_{\mathrm{ndx}}=2$$
4	1 2 3	3brtr4i	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<{+}_{\mathrm{ndx}}$$