This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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	$⊢ wrecs (R, A, F) = frecs (R, A, F \circ 2^{nd})$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cR	$class R$
1		cA	$class A$
2		cF	$class F$
3	1 0 2	cwrecs	$class wrecs (R, A, F)$
4		c2nd	$class 2^{nd}$
5	2 4	ccom	$class (F \circ 2^{nd})$
6	1 0 5	cfrecs	$class frecs (R, A, F \circ 2^{nd})$
7	3 6	wceq	$wff wrecs (R, A, F) = frecs (R, A, F \circ 2^{nd})$