Definition df-lsw 14194

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 14193	. 2 class lastS
2		vw	. . 3 setvar 𝑤
3		cvv 3422	. . 3 class V
4	2	cv 1538	. . . . . 6 class 𝑤
5		chash 13972	. . . . . 6 class ♯
6	4, 5	cfv 6418	. . . . 5 class (♯‘𝑤)
7		c1 10803	. . . . 5 class 1
8		cmin 11135	. . . . 5 class −
9	6, 7, 8	co 7255	. . . 4 class ((♯‘𝑤) − 1)
10	9, 4	cfv 6418	. . 3 class (𝑤‘((♯‘𝑤) − 1))
11	2, 3, 10	cmpt 5153	. 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))
12	1, 11	wceq 1539	1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1)))

This definition is referenced by:  lsw  14195  sseqval  32255  sseqfv1  32256  sseqfn  32257  sseqf  32259  sseqfv2  32261