Metamath Proof Explorer


Definition df-wrecs

Description: Define the well-ordered recursive function generator. This function takes the usual expressions from recursion theorems and forms a unified definition. Specifically, given a function F , a relation R , and a base set A , this definition generates a function G = wrecs ( R , A , F ) that has property that, at any point x e. A , ( Gx ) = ( F` ( G |`Pred ( R , A , x ) ) ) . See wfr1 , wfr2 , and wfr3 . (Contributed by Scott Fenton, 7-Jun-2018) (Revised by BJ, 27-Oct-2024)

Ref Expression
Assertion df-wrecs
|- wrecs ( R , A , F ) = frecs ( R , A , ( F o. 2nd ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cR
 |-  R
1 cA
 |-  A
2 cF
 |-  F
3 1 0 2 cwrecs
 |-  wrecs ( R , A , F )
4 c2nd
 |-  2nd
5 2 4 ccom
 |-  ( F o. 2nd )
6 1 0 5 cfrecs
 |-  frecs ( R , A , ( F o. 2nd ) )
7 3 6 wceq
 |-  wrecs ( R , A , F ) = frecs ( R , A , ( F o. 2nd ) )