Definition df-lsw 11149

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 11148	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 2800	. . 3 class V
4	2	cv 1394	. . . . . 6 class 𝑤
5		chash 11027	. . . . . 6 class ♯
6	4, 5	cfv 5324	. . . . 5 class (♯‘𝑤)
7		c1 8023	. . . . 5 class 1
8		cmin 8340	. . . . 5 class −
9	6, 7, 8	co 6013	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 5324	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 4148	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1395	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lswwrd  11150