Definition df-lsw 11158

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 11157	. 2 class lastS
2		vw	. . 3 setvar w
3		cvv 2802	. . 3 class _V
4	2	cv 1396	. . . . . 6 class w
5		chash 11036	. . . . . 6 class ♯
6	4, 5	cfv 5326	. . . . 5 class (♯ ` w )
7		c1 8032	. . . . 5 class 1
8		cmin 8349	. . . . 5 class -
9	6, 7, 8	co 6017	. . . 4 class ( (♯ ` w ) - 1 )
10	9, 4	cfv 5326	. . 3 class ( w ` ( (♯ ` w ) - 1 ) )
11	2, 3, 10	cmpt 4150	. 2 class ( w e. _V |-> ( w ` ( (♯ ` w ) - 1 ) ) )
12	1, 11	wceq 1397	1 wff lastS = ( w e. _V |-> ( w ` ( (♯ ` w ) - 1 ) ) )

This definition is referenced by:  lswwrd  11159