Definition df-lsw 14488

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 14487	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3440	. . 3 class V
4	2	cv 1540	. . . . . 6 class 𝑤
5		chash 14255	. . . . . 6 class ♯
6	4, 5	cfv 6492	. . . . 5 class (♯‘𝑤)
7		c1 11029	. . . . 5 class 1
8		cmin 11366	. . . . 5 class −
9	6, 7, 8	co 7358	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6492	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5179	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1541	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14489  sseqval  34547  sseqfv1  34548  sseqfn  34549  sseqf  34551  sseqfv2  34553