Definition df-lsw 14470

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 14469	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3436	. . 3 class V
4	2	cv 1539	. . . . . 6 class 𝑤
5		chash 14237	. . . . . 6 class ♯
6	4, 5	cfv 6482	. . . . 5 class (♯‘𝑤)
7		c1 11010	. . . . 5 class 1
8		cmin 11347	. . . . 5 class −
9	6, 7, 8	co 7349	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6482	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5173	. 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  14471  sseqval  34362  sseqfv1  34363  sseqfn  34364  sseqf  34366  sseqfv2  34368