Definition df-lsw 14631

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 14630	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3450	. . 3 class V
4	2	cv 1569	. . . . . 6 class 𝑤
5		chash 14397	. . . . . 6 class ♯
6	4, 5	cfv 6533	. . . . 5 class (♯‘𝑤)
7		c1 11128	. . . . 5 class 1
8		cmin 11468	. . . . 5 class −
9	6, 7, 8	co 7414	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6533	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5186	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1570	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is used by:  lsw  14632  sseqval  34902  sseqfv1  34903  sseqfn  34904  sseqf  34906  sseqfv2  34908