Definition df-lsw 14620

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 14619	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3457	. . 3 class V
4	2	cv 1569	. . . . . 6 class 𝑤
5		chash 14386	. . . . . 6 class ♯
6	4, 5	cfv 6540	. . . . 5 class (♯‘𝑤)
7		c1 11118	. . . . 5 class 1
8		cmin 11458	. . . . 5 class −
9	6, 7, 8	co 7419	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6540	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5194	. 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  14621  sseqval  34845  sseqfv1  34846  sseqfn  34847  sseqf  34849  sseqfv2  34851