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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 8029 for more details on why this definition is desirable. Unlike df-rdg 8029 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 8022 and recsval 8023 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 7990 | . 2 class recs(𝐹) |
3 | con0 6159 | . . 3 class On | |
4 | cep 5429 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 7929 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1538 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 7992 recseq 7993 nfrecs 7994 tfr1ALT 8019 tfr2ALT 8020 tfr3ALT 8021 csbrecsg 34745 |
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