Definition df-lsw 14484

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 14483	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3438	. . 3 class V
4	2	cv 1540	. . . . . 6 class 𝑤
5		chash 14251	. . . . . 6 class ♯
6	4, 5	cfv 6490	. . . . 5 class (♯‘𝑤)
7		c1 11025	. . . . 5 class 1
8		cmin 11362	. . . . 5 class −
9	6, 7, 8	co 7356	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6490	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5177	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1541	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14485  sseqval  34494  sseqfv1  34495  sseqfn  34496  sseqf  34498  sseqfv2  34500