Definition df-lsw 14601

Description: Extract the last symbol of a word. May be not meaningful for other sets which are not words. The name lastS (as abbreviation of "lastSymbol") is a compromise between usually used names for corresponding functions in computer programs (as last() or lastChar()), the terminology used for words in set.mm ("symbol" instead of "character") and brevity ("lastS" is shorter than "lastChar" and "lastSymbol"). Labels of theorems about last symbols of a word will contain the abbreviation "lsw" (Last Symbol of a Word). (Contributed by Alexander van der Vekens, 18-Mar-2018.)

Assertion

Ref	Expression
df-lsw	⊢ lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

Detailed syntax breakdown of Definition df-lsw

Step	Hyp	Ref	Expression
1		clsw 14600	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3480	. . 3 class V
4	2	cv 1539	. . . . . 6 class 𝑤
5		chash 14369	. . . . . 6 class ♯
6	4, 5	cfv 6561	. . . . 5 class (♯‘𝑤)
7		c1 11156	. . . . 5 class 1
8		cmin 11492	. . . . 5 class −
9	6, 7, 8	co 7431	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6561	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5225	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1540	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14602  sseqval  34390  sseqfv1  34391  sseqfn  34392  sseqf  34394  sseqfv2  34396