Definition df-lsw 14577

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 14576	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3455	. . 3 class V
4	2	cv 1560	. . . . . 6 class 𝑤
5		chash 14344	. . . . . 6 class ♯
6	4, 5	cfv 6522	. . . . 5 class (♯‘𝑤)
7		c1 11075	. . . . 5 class 1
8		cmin 11415	. . . . 5 class −
9	6, 7, 8	co 7397	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6522	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5182	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1561	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14578  sseqval  34686  sseqfv1  34687  sseqfn  34688  sseqf  34690  sseqfv2  34692