Definition df-lsw 13910

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 13909	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3491	. . 3 class V
4	2	cv 1535	. . . . . 6 class 𝑤
5		chash 13687	. . . . . 6 class ♯
6	4, 5	cfv 6348	. . . . 5 class (♯‘𝑤)
7		c1 10531	. . . . 5 class 1
8		cmin 10863	. . . . 5 class −
9	6, 7, 8	co 7149	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6348	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5139	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1536	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  13911  sseqval  31667  sseqfv1  31668  sseqfn  31669  sseqf  31671  sseqfv2  31673