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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 14600 | . 2 class lastS | |
| 2 | vw | . . 3 setvar 𝑤 | |
| 3 | cvv 3480 | . . 3 class V | |
| 4 | 2 | cv 1539 | . . . . . 6 class 𝑤 |
| 5 | chash 14369 | . . . . . 6 class ♯ | |
| 6 | 4, 5 | cfv 6561 | . . . . 5 class (♯‘𝑤) |
| 7 | c1 11156 | . . . . 5 class 1 | |
| 8 | cmin 11492 | . . . . 5 class − | |
| 9 | 6, 7, 8 | co 7431 | . . . 4 class ((♯‘𝑤) − 1) |
| 10 | 9, 4 | cfv 6561 | . . 3 class (𝑤‘((♯‘𝑤) − 1)) |
| 11 | 2, 3, 10 | cmpt 5225 | . 2 class (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
| 12 | 1, 11 | wceq 1540 | 1 wff lastS = (𝑤 ∈ V ↦ (𝑤‘((♯‘𝑤) − 1))) |
| Colors of variables: wff setvar class |
| This definition is referenced by: lsw 14602 sseqval 34390 sseqfv1 34391 sseqfn 34392 sseqf 34394 sseqfv2 34396 |
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