![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 7673 for more details on why this definition is desirable. Unlike df-rdg 7673 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 7666 and recsval 7667 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 7634 | . 2 class recs(𝐹) |
3 | con0 5882 | . . 3 class On | |
4 | cep 5176 | . . 3 class E | |
5 | 3, 4, 1 | cwrecs 7573 | . 2 class wrecs( E , On, 𝐹) |
6 | 2, 5 | wceq 1630 | 1 wff recs(𝐹) = wrecs( E , On, 𝐹) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrecs3 7636 recseq 7637 nfrecs 7638 tfr1ALT 7663 tfr2ALT 7664 tfr3ALT 7665 csbrecsg 33483 |
Copyright terms: Public domain | W3C validator |