Definition df-lsw 14517

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 14516	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3431	. . 3 class V
4	2	cv 1546	. . . . . 6 class 𝑤
5		chash 14284	. . . . . 6 class ♯
6	4, 5	cfv 6486	. . . . 5 class (♯‘𝑤)
7		c1 11031	. . . . 5 class 1
8		cmin 11369	. . . . 5 class −
9	6, 7, 8	co 7357	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6486	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5154	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1547	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14518  sseqval  34581  sseqfv1  34582  sseqfn  34583  sseqf  34585  sseqfv2  34587