MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-lsw Structured version   Unicode version

Definition df-lsw 12663
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
StepHypRef Expression
1 clsw 12655 . 2  class lastS
2 vw . . 3  setvar  w
3 cvv 3082 . . 3  class  _V
42cv 1437 . . . . . 6  class  w
5 chash 12516 . . . . . 6  class  #
64, 5cfv 5599 . . . . 5  class  ( # `  w )
7 c1 9542 . . . . 5  class  1
8 cmin 9862 . . . . 5  class  -
96, 7, 8co 6303 . . . 4  class  ( (
# `  w )  -  1 )
109, 4cfv 5599 . . 3  class  ( w `
 ( ( # `  w )  -  1 ) )
112, 3, 10cmpt 4480 . 2  class  ( w  e.  _V  |->  ( w `
 ( ( # `  w )  -  1 ) ) )
121, 11wceq 1438 1  wff lastS  =  ( w  e.  _V  |->  ( w `  ( (
# `  w )  -  1 ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  lsw  12709  sseqval  29223  sseqfv1  29224  sseqfn  29225  sseqf  29227  sseqfv2  29229
  Copyright terms: Public domain W3C validator