Definition df-lsw 13624

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 13623	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3415	. . 3 class V
4	2	cv 1657	. . . . . 6 class 𝑤
5		chash 13411	. . . . . 6 class ♯
6	4, 5	cfv 6124	. . . . 5 class (♯‘𝑤)
7		c1 10254	. . . . 5 class 1
8		cmin 10586	. . . . 5 class −
9	6, 7, 8	co 6906	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6124	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 4953	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1658	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  13625  sseqval  30997  sseqfv1  30998  sseqfn  30999  sseqf  31001  sseqfv2  31003