Definition df-lsw 14611

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 14610	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3488	. . 3 class V
4	2	cv 1536	. . . . . 6 class 𝑤
5		chash 14379	. . . . . 6 class ♯
6	4, 5	cfv 6573	. . . . 5 class (♯‘𝑤)
7		c1 11185	. . . . 5 class 1
8		cmin 11520	. . . . 5 class −
9	6, 7, 8	co 7448	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6573	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5249	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1537	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14612  sseqval  34353  sseqfv1  34354  sseqfn  34355  sseqf  34357  sseqfv2  34359