Definition df-lsw 14510

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 14509	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3475	. . 3 class V
4	2	cv 1541	. . . . . 6 class 𝑤
5		chash 14287	. . . . . 6 class ♯
6	4, 5	cfv 6541	. . . . 5 class (♯‘𝑤)
7		c1 11108	. . . . 5 class 1
8		cmin 11441	. . . . 5 class −
9	6, 7, 8	co 7406	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6541	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5231	. 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  14511  sseqval  33376  sseqfv1  33377  sseqfn  33378  sseqf  33380  sseqfv2  33382