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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 8437 for more details on why this definition is desirable. Unlike df-rdg 8437 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 8430 and recsval 8431 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 8397 | . 2 class recs(𝐹) |
3 | con0 6374 | . . 3 class On | |
4 | cep 5585 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 8323 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1533 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 8399 dfrecs3OLD 8400 recseq 8401 nfrecs 8402 tfr1ALT 8427 tfr2ALT 8428 tfr3ALT 8429 csbrecsg 36840 |
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