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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 7848 for more details on why this definition is desirable. Unlike df-rdg 7848 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 7841 and recsval 7842 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 7809 | . 2 class recs(𝐹) |
3 | con0 6026 | . . 3 class On | |
4 | cep 5312 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 7747 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1508 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 7811 recseq 7812 nfrecs 7813 tfr1ALT 7838 tfr2ALT 7839 tfr3ALT 7840 csbrecsg 34088 |
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