Definition df-lsw 13918

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 13917	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3497	. . 3 class V
4	2	cv 1535	. . . . . 6 class 𝑤
5		chash 13693	. . . . . 6 class ♯
6	4, 5	cfv 6358	. . . . 5 class (♯‘𝑤)
7		c1 10541	. . . . 5 class 1
8		cmin 10873	. . . . 5 class −
9	6, 7, 8	co 7159	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6358	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5149	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1536	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  13919  sseqval  31650  sseqfv1  31651  sseqfn  31652  sseqf  31654  sseqfv2  31656