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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 14509 | . 2 class lastS | |
2 | vw | . . 3 setvar 𝑤 | |
3 | cvv 3475 | . . 3 class V | |
4 | 2 | cv 1541 | . . . . . 6 class 𝑤 |
5 | chash 14287 | . . . . . 6 class ♯ | |
6 | 4, 5 | cfv 6541 | . . . . 5 class (♯‘𝑤) |
7 | c1 11108 | . . . . 5 class 1 | |
8 | cmin 11441 | . . . . 5 class − | |
9 | 6, 7, 8 | co 7406 | . . . 4 class ((♯‘𝑤) − 1) |
10 | 9, 4 | cfv 6541 | . . 3 class (𝑤‘((♯‘𝑤) − 1)) |
11 | 2, 3, 10 | cmpt 5231 | . 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
12 | 1, 11 | wceq 1542 | 1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
Colors of variables: wff setvar class |
This definition is referenced by: lsw 14511 sseqval 33376 sseqfv1 33377 sseqfn 33378 sseqf 33380 sseqfv2 33382 |
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