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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 13904 | . 2 class lastS | |
2 | vw | . . 3 setvar 𝑤 | |
3 | cvv 3495 | . . 3 class V | |
4 | 2 | cv 1527 | . . . . . 6 class 𝑤 |
5 | chash 13680 | . . . . . 6 class ♯ | |
6 | 4, 5 | cfv 6349 | . . . . 5 class (♯‘𝑤) |
7 | c1 10527 | . . . . 5 class 1 | |
8 | cmin 10859 | . . . . 5 class − | |
9 | 6, 7, 8 | co 7145 | . . . 4 class ((♯‘𝑤) − 1) |
10 | 9, 4 | cfv 6349 | . . 3 class (𝑤‘((♯‘𝑤) − 1)) |
11 | 2, 3, 10 | cmpt 5138 | . 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
12 | 1, 11 | wceq 1528 | 1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
Colors of variables: wff setvar class |
This definition is referenced by: lsw 13906 sseqval 31546 sseqfv1 31547 sseqfn 31548 sseqf 31550 sseqfv2 31552 |
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