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Mirrors > Home > MPE Home > Th. List > df-lsw | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-lsw | ⊢ lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clsw 13623 | . 2 class lastS | |
2 | vw | . . 3 setvar 𝑤 | |
3 | cvv 3415 | . . 3 class V | |
4 | 2 | cv 1657 | . . . . . 6 class 𝑤 |
5 | chash 13411 | . . . . . 6 class ♯ | |
6 | 4, 5 | cfv 6124 | . . . . 5 class (♯‘𝑤) |
7 | c1 10254 | . . . . 5 class 1 | |
8 | cmin 10586 | . . . . 5 class − | |
9 | 6, 7, 8 | co 6906 | . . . 4 class ((♯‘𝑤) − 1) |
10 | 9, 4 | cfv 6124 | . . 3 class (𝑤‘((♯‘𝑤) − 1)) |
11 | 2, 3, 10 | cmpt 4953 | . 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
12 | 1, 11 | wceq 1658 | 1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
Colors of variables: wff setvar class |
This definition is referenced by: lsw 13625 sseqval 30997 sseqfv1 30998 sseqfn 30999 sseqf 31001 sseqfv2 31003 |
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