Definition df-lsw 14596

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 14595	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3455	. . 3 class V
4	2	cv 1569	. . . . . 6 class 𝑤
5		chash 14362	. . . . . 6 class ♯
6	4, 5	cfv 6536	. . . . 5 class (♯‘𝑤)
7		c1 11096	. . . . 5 class 1
8		cmin 11436	. . . . 5 class −
9	6, 7, 8	co 7410	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6536	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5192	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1570	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14597  sseqval  34778  sseqfv1  34779  sseqfn  34780  sseqf  34782  sseqfv2  34784