Definition df-lsw 14498

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 14497	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3442	. . 3 class V
4	2	cv 1541	. . . . . 6 class 𝑤
5		chash 14265	. . . . . 6 class ♯
6	4, 5	cfv 6500	. . . . 5 class (♯‘𝑤)
7		c1 11039	. . . . 5 class 1
8		cmin 11376	. . . . 5 class −
9	6, 7, 8	co 7368	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6500	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5181	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1542	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14499  sseqval  34570  sseqfv1  34571  sseqfn  34572  sseqf  34574  sseqfv2  34576