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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 8046 for more details on why this definition is desirable. Unlike df-rdg 8046 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 8039 and recsval 8040 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 8007 | . 2 class recs(𝐹) |
3 | con0 6191 | . . 3 class On | |
4 | cep 5464 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 7946 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1537 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 8009 recseq 8010 nfrecs 8011 tfr1ALT 8036 tfr2ALT 8037 tfr3ALT 8038 csbrecsg 34612 |
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