Definition df-lsw 14519

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 14518	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3430	. . 3 class V
4	2	cv 1541	. . . . . 6 class 𝑤
5		chash 14286	. . . . . 6 class ♯
6	4, 5	cfv 6493	. . . . 5 class (♯‘𝑤)
7		c1 11033	. . . . 5 class 1
8		cmin 11371	. . . . 5 class −
9	6, 7, 8	co 7361	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6493	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5167	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1542	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14520  sseqval  34551  sseqfv1  34552  sseqfn  34553  sseqf  34555  sseqfv2  34557