Definition df-lsw 11295

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 11294	. 2 class lastS
2		vw	. . 3 setvar w
3		cvv 2815	. . 3 class _V
4	2	cv 1397	. . . . . 6 class w
5		chash 11163	. . . . . 6 class ♯
6	4, 5	cfv 5357	. . . . 5 class (♯ ` w )
7		c1 8144	. . . . 5 class 1
8		cmin 8460	. . . . 5 class -
9	6, 7, 8	co 6058	. . . 4 class ( (♯ ` w ) - 1 )
10	9, 4	cfv 5357	. . 3 class ( w ` ( (♯ ` w ) - 1 ) )
11	2, 3, 10	cmpt 4176	. 2 class ( w e. _V |-> ( w ` ( (♯ ` w ) - 1 ) ) )
12	1, 11	wceq 1398	1 wff lastS = ( w e. _V |-> ( w ` ( (♯ ` w ) - 1 ) ) )

This definition is referenced by:  lswwrd  11296