Description: Law of well-founded recursion over a partial order, part one. Establish the functionality and domain of the recursive function generator. Note that by requiring a partial order we can avoid using the axiom of infinity. (Contributed by Scott Fenton, 11-Sep-2023)
Ref | Expression | ||
---|---|---|---|
Hypothesis | fprr.1 | |
|
Assertion | fpr1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fprr.1 | |
|
2 | eqid | |
|
3 | 2 | frrlem1 | |
4 | 3 1 | fprlem1 | |
5 | 3 1 4 | frrlem9 | |
6 | eqid | |
|
7 | simp1 | |
|
8 | ssidd | |
|
9 | fprlem2 | |
|
10 | setlikespec | |
|
11 | 10 | ancoms | |
12 | 11 | 3ad2antl3 | |
13 | predss | |
|
14 | 13 | a1i | |
15 | difssd | |
|
16 | simpr | |
|
17 | 15 16 | jca | |
18 | frpomin2 | |
|
19 | 17 18 | syldan | |
20 | 3 1 4 6 7 8 9 12 14 19 | frrlem14 | |
21 | df-fn | |
|
22 | 5 20 21 | sylanbrc | |