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| Mirrors > Home > MPE Home > Th. List > df-recs | Structured version Visualization version GIF version | ||
| Description: Define a function recs(𝐹) on On, the class of ordinal numbers, by transfinite recursion given a rule 𝐹 which sets the next value given all values so far. See df-rdg 8450 for more details on why this definition is desirable. Unlike df-rdg 8450 which restricts the update rule to use only the previous value, this version allows the update rule to use all previous values, which is why it is described as "strong", although it is actually more primitive. See recsfnon 8443 and recsval 8444 for the primary contract of this definition. (Contributed by Stefan O'Rear, 18-Jan-2015.) (Revised by Scott Fenton, 3-Aug-2020.) |
| Ref | Expression |
|---|---|
| df-recs | ⊢ recs(𝐹) = wrecs( E , On, 𝐹) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cF | . . 3 class 𝐹 | |
| 2 | 1 | crecs 8410 | . 2 class recs(𝐹) |
| 3 | con0 6384 | . . 3 class On | |
| 4 | cep 5583 | . . 3 class E | |
| 5 | 3, 4, 1 | cwrecs 8336 | . 2 class wrecs( E , On, 𝐹) |
| 6 | 2, 5 | wceq 1540 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
| Colors of variables: wff setvar class |
| This definition is referenced by: dfrecs3 8412 dfrecs3OLD 8413 recseq 8414 nfrecs 8415 tfr1ALT 8440 tfr2ALT 8441 tfr3ALT 8442 csbrecsg 37329 |
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