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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 8440 for more details on why this definition is desirable. Unlike df-rdg 8440 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 8433 and recsval 8434 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 8400 | . 2 class recs(𝐹) |
3 | con0 6376 | . . 3 class On | |
4 | cep 5585 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 8326 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1534 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 8402 dfrecs3OLD 8403 recseq 8404 nfrecs 8405 tfr1ALT 8430 tfr2ALT 8431 tfr3ALT 8432 csbrecsg 37035 |
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