Definition df-lsw 13300

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 13292	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3200	. . 3 class V
4	2	cv 1482	. . . . . 6 class 𝑤
5		chash 13117	. . . . . 6 class #
6	4, 5	cfv 5888	. . . . 5 class (#‘𝑤)
7		c1 9937	. . . . 5 class 1
8		cmin 10266	. . . . 5 class −
9	6, 7, 8	co 6650	. . . 4 class ((#‘𝑤) − 1)
10	9, 4	cfv 5888	. . 3 class (𝑤‘((#‘𝑤) − 1))
11	2, 3, 10	cmpt 4729	. 2 class (𝑤 ∈ V ↦ (𝑤‘((#‘𝑤) − 1)))
12	1, 11	wceq 1483	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((#‘𝑤) − 1)))

This definition is referenced by:  lsw  13351  sseqval  30450  sseqfv1  30451  sseqfn  30452  sseqf  30454  sseqfv2  30456