Definition df-lsw 14528

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 14527	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3447	. . 3 class V
4	2	cv 1539	. . . . . 6 class 𝑤
5		chash 14295	. . . . . 6 class ♯
6	4, 5	cfv 6511	. . . . 5 class (♯‘𝑤)
7		c1 11069	. . . . 5 class 1
8		cmin 11405	. . . . 5 class −
9	6, 7, 8	co 7387	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6511	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5188	. 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  14529  sseqval  34379  sseqfv1  34380  sseqfn  34381  sseqf  34383  sseqfv2  34385