Definition df-lsw 14525

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 14524	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3429	. . 3 class V
4	2	cv 1541	. . . . . 6 class 𝑤
5		chash 14292	. . . . . 6 class ♯
6	4, 5	cfv 6498	. . . . 5 class (♯‘𝑤)
7		c1 11039	. . . . 5 class 1
8		cmin 11377	. . . . 5 class −
9	6, 7, 8	co 7367	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6498	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5166	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1542	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14526  sseqval  34532  sseqfv1  34533  sseqfn  34534  sseqf  34536  sseqfv2  34538