Definition df-lsw 14709

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 14708	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3450	. . 3 class V
4	2	cv 1568	. . . . . 6 class 𝑤
5		chash 14475	. . . . . 6 class ♯
6	4, 5	cfv 6538	. . . . 5 class (♯‘𝑤)
7		c1 11202	. . . . 5 class 1
8		cmin 11542	. . . . 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 5185	. 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  14710  sseqval  35063  sseqfv1  35064  sseqfn  35065  sseqf  35067  sseqfv2  35069