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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 7393 for more details on why this definition is desirable. Unlike df-rdg 7393 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 7386 and recsval 7387 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 7354 | . 2 class recs(𝐹) |
3 | con0 5640 | . . 3 class On | |
4 | cep 4947 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 7293 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1475 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 7356 recseq 7357 nfrecs 7358 tfr1ALT 7383 tfr2ALT 7384 tfr3ALT 7385 csbrecsg 32350 |
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