Definition df-lsw 14581

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 14580	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3459	. . 3 class V
4	2	cv 1539	. . . . . 6 class 𝑤
5		chash 14348	. . . . . 6 class ♯
6	4, 5	cfv 6531	. . . . 5 class (♯‘𝑤)
7		c1 11130	. . . . 5 class 1
8		cmin 11466	. . . . 5 class −
9	6, 7, 8	co 7405	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6531	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5201	. 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  14582  sseqval  34420  sseqfv1  34421  sseqfn  34422  sseqf  34424  sseqfv2  34426