Definition df-lsw 14721

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 14720	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3454	. . 3 class V
4	2	cv 1568	. . . . . 6 class 𝑤
5		chash 14487	. . . . . 6 class ♯
6	4, 5	cfv 6547	. . . . 5 class (♯‘𝑤)
7		c1 11214	. . . . 5 class 1
8		cmin 11554	. . . . 5 class −
9	6, 7, 8	co 7430	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6547	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5189	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1569	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is used by:  lsw  14722  sseqval  35076  sseqfv1  35077  sseqfn  35078  sseqf  35080  sseqfv2  35082