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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 8037 for more details on why this definition is desirable. Unlike df-rdg 8037 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 8030 and recsval 8031 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 7998 | . 2 class recs(𝐹) |
3 | con0 6185 | . . 3 class On | |
4 | cep 5458 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 7937 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1528 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 8000 recseq 8001 nfrecs 8002 tfr1ALT 8027 tfr2ALT 8028 tfr3ALT 8029 csbrecsg 34492 |
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