Definition df-lsw 14535

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 14534	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3450	. . 3 class V
4	2	cv 1539	. . . . . 6 class 𝑤
5		chash 14302	. . . . . 6 class ♯
6	4, 5	cfv 6514	. . . . 5 class (♯‘𝑤)
7		c1 11076	. . . . 5 class 1
8		cmin 11412	. . . . 5 class −
9	6, 7, 8	co 7390	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6514	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5191	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1540	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14536  sseqval  34386  sseqfv1  34387  sseqfn  34388  sseqf  34390  sseqfv2  34392