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 ∘ 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 ∘ 2nd )
6	1 0 5	cfrecs	⊢ frecs ( 𝑅 , 𝐴 , ( 𝐹 ∘ 2nd ) )
7	3 6	wceq	⊢ wrecs ( 𝑅 , 𝐴 , 𝐹 ) = frecs ( 𝑅 , 𝐴 , ( 𝐹 ∘ 2nd ) )