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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 13905 | . 2 class lastS | |
2 | vw | . . 3 setvar 𝑤 | |
3 | cvv 3441 | . . 3 class V | |
4 | 2 | cv 1537 | . . . . . 6 class 𝑤 |
5 | chash 13686 | . . . . . 6 class ♯ | |
6 | 4, 5 | cfv 6324 | . . . . 5 class (♯‘𝑤) |
7 | c1 10527 | . . . . 5 class 1 | |
8 | cmin 10859 | . . . . 5 class − | |
9 | 6, 7, 8 | co 7135 | . . . 4 class ((♯‘𝑤) − 1) |
10 | 9, 4 | cfv 6324 | . . 3 class (𝑤‘((♯‘𝑤) − 1)) |
11 | 2, 3, 10 | cmpt 5110 | . 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
12 | 1, 11 | wceq 1538 | 1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
Colors of variables: wff setvar class |
This definition is referenced by: lsw 13907 sseqval 31756 sseqfv1 31757 sseqfn 31758 sseqf 31760 sseqfv2 31762 |
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