MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-recs Structured version   Visualization version   GIF version

Definition df-recs 7513
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 7551 for more details on why this definition is desirable. Unlike df-rdg 7551 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 7544 and recsval 7545 for the primary contract of this definition. (Contributed by Stefan O'Rear, 18-Jan-2015.) (Revised by Scott Fenton, 3-Aug-2020.)
Assertion
Ref Expression
df-recs recs(𝐹) = wrecs( E , On, 𝐹)

Detailed syntax breakdown of Definition df-recs
StepHypRef Expression
1 cF . . 3 class 𝐹
21crecs 7512 . 2 class recs(𝐹)
3 con0 5761 . . 3 class On
4 cep 5057 . . 3 class E
53, 4, 1cwrecs 7451 . 2 class wrecs( E , On, 𝐹)
62, 5wceq 1523 1 wff recs(𝐹) = wrecs( E , On, 𝐹)
Colors of variables: wff setvar class
This definition is referenced by:  dfrecs3  7514  recseq  7515  nfrecs  7516  tfr1ALT  7541  tfr2ALT  7542  tfr3ALT  7543  csbrecsg  33304
  Copyright terms: Public domain W3C validator