Definition df-lsw 14513

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 14512	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3475	. . 3 class V
4	2	cv 1541	. . . . . 6 class 𝑤
5		chash 14290	. . . . . 6 class ♯
6	4, 5	cfv 6544	. . . . 5 class (♯‘𝑤)
7		c1 11111	. . . . 5 class 1
8		cmin 11444	. . . . 5 class −
9	6, 7, 8	co 7409	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6544	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5232	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1542	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14514  sseqval  33387  sseqfv1  33388  sseqfn  33389  sseqf  33391  sseqfv2  33393