Definition df-lsw 13155

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 13147	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3173	. . 3 class V
4	2	cv 1474	. . . . . 6 class 𝑤
5		chash 12979	. . . . . 6 class #
6	4, 5	cfv 5804	. . . . 5 class (#‘𝑤)
7		c1 9816	. . . . 5 class 1
8		cmin 10145	. . . . 5 class −
9	6, 7, 8	co 6549	. . . 4 class ((#‘𝑤) − 1)
10	9, 4	cfv 5804	. . 3 class (𝑤‘((#‘𝑤) − 1))
11	2, 3, 10	cmpt 4643	. 2 class (𝑤 ∈ V ↦ (𝑤‘((#‘𝑤) − 1)))
12	1, 11	wceq 1475	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((#‘𝑤) − 1)))

This definition is referenced by:  lsw  13204  sseqval  29777  sseqfv1  29778  sseqfn  29779  sseqf  29781  sseqfv2  29783