Definition df-lsw 14708

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 14707	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3451	. . 3 class V
4	2	cv 1569	. . . . . 6 class 𝑤
5		chash 14474	. . . . . 6 class ♯
6	4, 5	cfv 6538	. . . . 5 class (♯‘𝑤)
7		c1 11201	. . . . 5 class 1
8		cmin 11541	. . . . 5 class −
9	6, 7, 8	co 7420	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6538	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5186	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1570	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is used by:  lsw  14709  sseqval  35020  sseqfv1  35021  sseqfn  35022  sseqf  35024  sseqfv2  35026