Definition df-lsw 13962

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 13961	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3409	. . 3 class V
4	2	cv 1537	. . . . . 6 class 𝑤
5		chash 13740	. . . . . 6 class ♯
6	4, 5	cfv 6335	. . . . 5 class (♯‘𝑤)
7		c1 10576	. . . . 5 class 1
8		cmin 10908	. . . . 5 class −
9	6, 7, 8	co 7150	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6335	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5112	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1538	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  13963  sseqval  31874  sseqfv1  31875  sseqfn  31876  sseqf  31878  sseqfv2  31880