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	⊢ ( Base ‘ ndx ) < ( dist ‘ ndx )

Proof

Step	Hyp	Ref	Expression
1		1nn	⊢ 1 ∈ ℕ
2		2nn0	⊢ 2 ∈ ℕ0
3		1nn0	⊢ 1 ∈ ℕ0
4		1lt10	⊢ 1 < ; 1 0
5	1 2 3 4	declti	⊢ 1 < ; 1 2
6		basendx	⊢ ( Base ‘ ndx ) = 1
7		dsndx	⊢ ( dist ‘ ndx ) = ; 1 2
8	5 6 7	3brtr4i	⊢ ( Base ‘ ndx ) < ( dist ‘ ndx )