Definition df-lsw 13332

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 13324	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3231	. . 3 class V
4	2	cv 1522	. . . . . 6 class 𝑤
5		chash 13157	. . . . . 6 class #
6	4, 5	cfv 5926	. . . . 5 class (#‘𝑤)
7		c1 9975	. . . . 5 class 1
8		cmin 10304	. . . . 5 class −
9	6, 7, 8	co 6690	. . . 4 class ((#‘𝑤) − 1)
10	9, 4	cfv 5926	. . 3 class (𝑤‘((#‘𝑤) − 1))
11	2, 3, 10	cmpt 4762	. 2 class (𝑤 ∈ V ↦ (𝑤‘((#‘𝑤) − 1)))
12	1, 11	wceq 1523	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((#‘𝑤) − 1)))

This definition is referenced by:  lsw  13384  sseqval  30578  sseqfv1  30579  sseqfn  30580  sseqf  30582  sseqfv2  30584