Definition df-lsw 14566

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 14565	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3462	. . 3 class V
4	2	cv 1533	. . . . . 6 class 𝑤
5		chash 14342	. . . . . 6 class ♯
6	4, 5	cfv 6546	. . . . 5 class (♯‘𝑤)
7		c1 11150	. . . . 5 class 1
8		cmin 11485	. . . . 5 class −
9	6, 7, 8	co 7416	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6546	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5228	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1534	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14567  sseqval  34235  sseqfv1  34236  sseqfn  34237  sseqf  34239  sseqfv2  34241