Definition df-lsw 14275

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 14274	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3433	. . 3 class V
4	2	cv 1538	. . . . . 6 class 𝑤
5		chash 14053	. . . . . 6 class ♯
6	4, 5	cfv 6437	. . . . 5 class (♯‘𝑤)
7		c1 10881	. . . . 5 class 1
8		cmin 11214	. . . . 5 class −
9	6, 7, 8	co 7284	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6437	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5158	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1539	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14276  sseqval  32364  sseqfv1  32365  sseqfn  32366  sseqf  32368  sseqfv2  32370