Definition df-lsw 14597

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 14596	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3477	. . 3 class V
4	2	cv 1535	. . . . . 6 class 𝑤
5		chash 14365	. . . . . 6 class ♯
6	4, 5	cfv 6562	. . . . 5 class (♯‘𝑤)
7		c1 11153	. . . . 5 class 1
8		cmin 11489	. . . . 5 class −
9	6, 7, 8	co 7430	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6562	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5230	. 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  14598  sseqval  34369  sseqfv1  34370  sseqfn  34371  sseqf  34373  sseqfv2  34375