Theorem basendxltdsndx

Description: The index of the slot for the base set is less then the index of the slot for the distance in an extensible structure. Formerly part of proof for tmslem . (Contributed by AV, 28-Oct-2024)

	Ref	Expression
Assertion	basendxltdsndx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<\mathrm{dist}\left(\mathrm{ndx}\right)$$

Proof

Step	Hyp	Ref	Expression
1		1nn	$$⊢1\in \mathbb{N}$$
2		2nn0	$$⊢2\in {\mathbb{N}}_0$$
3		1nn0	$$⊢1\in {\mathbb{N}}_0$$
4		1lt10	$$⊢1<10$$
5	1 2 3 4	declti	$$⊢1<12$$
6		basendx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}=1$$
7		dsndx	$$⊢\mathrm{dist}\left(\mathrm{ndx}\right)=12$$
8	5 6 7	3brtr4i	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<\mathrm{dist}\left(\mathrm{ndx}\right)$$