Definition df-lsw 13531

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 13523	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3402	. . 3 class V
4	2	cv 1636	. . . . . 6 class 𝑤
5		chash 13357	. . . . . 6 class ♯
6	4, 5	cfv 6111	. . . . 5 class (♯‘𝑤)
7		c1 10232	. . . . 5 class 1
8		cmin 10561	. . . . 5 class −
9	6, 7, 8	co 6884	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6111	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 4934	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1637	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  13583  sseqval  30798  sseqfv1  30799  sseqfn  30800  sseqf  30802  sseqfv2  30804