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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 14565 | . 2 class lastS | |
2 | vw | . . 3 setvar 𝑤 | |
3 | cvv 3462 | . . 3 class V | |
4 | 2 | cv 1533 | . . . . . 6 class 𝑤 |
5 | chash 14342 | . . . . . 6 class ♯ | |
6 | 4, 5 | cfv 6546 | . . . . 5 class (♯‘𝑤) |
7 | c1 11150 | . . . . 5 class 1 | |
8 | cmin 11485 | . . . . 5 class − | |
9 | 6, 7, 8 | co 7416 | . . . 4 class ((♯‘𝑤) − 1) |
10 | 9, 4 | cfv 6546 | . . 3 class (𝑤‘((♯‘𝑤) − 1)) |
11 | 2, 3, 10 | cmpt 5228 | . 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
12 | 1, 11 | wceq 1534 | 1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
Colors of variables: wff setvar class |
This definition is referenced by: lsw 14567 sseqval 34235 sseqfv1 34236 sseqfn 34237 sseqf 34239 sseqfv2 34241 |
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