Definition df-lsw 14600

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 14599	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3463	. . 3 class V
4	2	cv 1566	. . . . . 6 class 𝑤
5		chash 14366	. . . . . 6 class ♯
6	4, 5	cfv 6537	. . . . 5 class (♯‘𝑤)
7		c1 11101	. . . . 5 class 1
8		cmin 11441	. . . . 5 class −
9	6, 7, 8	co 7411	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6537	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5196	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1567	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14601  sseqval  34723  sseqfv1  34724  sseqfn  34725  sseqf  34727  sseqfv2  34729