Description: Lemma for resubeu . A value which when added to A , results in B . (Contributed by Steven Nguyen, 7-Jan-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | resubeulem2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | renegid | |
|
2 | 1 | adantr | |
3 | 2 | oveq1d | |
4 | simpl | |
|
5 | 4 | recnd | |
6 | rernegcl | |
|
7 | 6 | adantr | |
8 | 7 | recnd | |
9 | elre0re | |
|
10 | 9 9 | readdcld | |
11 | rernegcl | |
|
12 | 10 11 | syl | |
13 | id | |
|
14 | 12 13 | readdcld | |
15 | 14 | adantl | |
16 | 15 | recnd | |
17 | 5 8 16 | addassd | |
18 | resubeulem1 | |
|
19 | 18 | oveq1d | |
20 | 9 | recnd | |
21 | 12 | recnd | |
22 | recn | |
|
23 | 20 21 22 | addassd | |
24 | reneg0addid2 | |
|
25 | 19 23 24 | 3eqtr3d | |
26 | 25 | adantl | |
27 | 3 17 26 | 3eqtr3d | |