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Definition df-wrecs 8337
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 𝑥𝐴, (𝐺𝑥) = (𝐹‘(𝐺 ↾ Pred(𝑅, 𝐴, 𝑥))). See wfr1 8375, wfr2 8376, and wfr3 8377. (Contributed by Scott Fenton, 7-Jun-2018.) (Revised by BJ, 27-Oct-2024.)
Assertion
Ref Expression
df-wrecs wrecs(𝑅, 𝐴, 𝐹) = frecs(𝑅, 𝐴, (𝐹 ∘ 2nd ))

Detailed syntax breakdown of Definition df-wrecs
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cR . . 3 class 𝑅
3 cF . . 3 class 𝐹
41, 2, 3cwrecs 8336 . 2 class wrecs(𝑅, 𝐴, 𝐹)
5 c2nd 8013 . . . 4 class 2nd
63, 5ccom 5689 . . 3 class (𝐹 ∘ 2nd )
71, 2, 6cfrecs 8305 . 2 class frecs(𝑅, 𝐴, (𝐹 ∘ 2nd ))
84, 7wceq 1540 1 wff wrecs(𝑅, 𝐴, 𝐹) = frecs(𝑅, 𝐴, (𝐹 ∘ 2nd ))
Colors of variables: wff setvar class
This definition is referenced by:  dfwrecsOLD  8338  wrecseq123  8339  nfwrecs  8341  csbwrecsg  8346  wfrrel  8369  wfrdmss  8370  wfrdmcl  8371  wfrfun  8372  wfrresex  8373  wfr2a  8374  wfr1  8375  dfrecs3  8412
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