Definition df-lsw 14504

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 14503	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3444	. . 3 class V
4	2	cv 1539	. . . . . 6 class 𝑤
5		chash 14271	. . . . . 6 class ♯
6	4, 5	cfv 6499	. . . . 5 class (♯‘𝑤)
7		c1 11045	. . . . 5 class 1
8		cmin 11381	. . . . 5 class −
9	6, 7, 8	co 7369	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6499	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5183	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1540	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14505  sseqval  34372  sseqfv1  34373  sseqfn  34374  sseqf  34376  sseqfv2  34378