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Mirrors > Home > MPE Home > Th. List > df-wrecs | Structured version Visualization version Unicode version |
Description: Here we define the well-founded recursive function generator. This function takes the usual expressions from recursion theorems and forms a unified definition. Specifically, given a function , a relationship , and a base set , this definition generates a function wrecs that has property that, at any point , . See wfr1 7433, wfr2 7434, and wfr3 7435. (Contributed by Scott Fenton, 7-Jun-2018.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-wrecs | wrecs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | cR | . . 3 | |
3 | cF | . . 3 | |
4 | 1, 2, 3 | cwrecs 7406 | . 2 wrecs |
5 | vf | . . . . . . . 8 | |
6 | 5 | cv 1482 | . . . . . . 7 |
7 | vx | . . . . . . . 8 | |
8 | 7 | cv 1482 | . . . . . . 7 |
9 | 6, 8 | wfn 5883 | . . . . . 6 |
10 | 8, 1 | wss 3574 | . . . . . . 7 |
11 | vy | . . . . . . . . . . 11 | |
12 | 11 | cv 1482 | . . . . . . . . . 10 |
13 | 1, 2, 12 | cpred 5679 | . . . . . . . . 9 |
14 | 13, 8 | wss 3574 | . . . . . . . 8 |
15 | 14, 11, 8 | wral 2912 | . . . . . . 7 |
16 | 10, 15 | wa 384 | . . . . . 6 |
17 | 12, 6 | cfv 5888 | . . . . . . . 8 |
18 | 6, 13 | cres 5116 | . . . . . . . . 9 |
19 | 18, 3 | cfv 5888 | . . . . . . . 8 |
20 | 17, 19 | wceq 1483 | . . . . . . 7 |
21 | 20, 11, 8 | wral 2912 | . . . . . 6 |
22 | 9, 16, 21 | w3a 1037 | . . . . 5 |
23 | 22, 7 | wex 1704 | . . . 4 |
24 | 23, 5 | cab 2608 | . . 3 |
25 | 24 | cuni 4436 | . 2 |
26 | 4, 25 | wceq 1483 | 1 wrecs |
Colors of variables: wff setvar class |
This definition is referenced by: wrecseq123 7408 nfwrecs 7409 wfrrel 7420 wfrdmss 7421 wfrdmcl 7423 wfrfun 7425 wfrlem12 7426 wfrlem16 7430 wfrlem17 7431 dfrecs3 7469 csbwrecsg 33173 |
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