Definition df-lsw 11350

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 e. _V |-> ( w ` ( (♯ ` w ) - 1 ) ) )

Detailed syntax breakdown of Definition df-lsw

Step	Hyp	Ref	Expression
1		clsw 11349	. 2 class lastS
2		vw	. . 3 setvar w
3		cvv 2821	. . 3 class _V
4	2	cv 1401	. . . . . 6 class w
5		chash 11214	. . . . . 6 class ♯
6	4, 5	cfv 5377	. . . . 5 class (♯ ` w )
7		c1 8180	. . . . 5 class 1
8		cmin 8497	. . . . 5 class -
9	6, 7, 8	co 6085	. . . 4 class ( (♯ ` w ) - 1 )
10	9, 4	cfv 5377	. . 3 class ( w ` ( (♯ ` w ) - 1 ) )
11	2, 3, 10	cmpt 4192	. 2 class ( w e. _V |-> ( w ` ( (♯ ` w ) - 1 ) ) )
12	1, 11	wceq 1402	1 wff lastS = ( w e. _V |-> ( w ` ( (♯ ` w ) - 1 ) ) )

This definition is used by:  lswwrd  11351