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Mirrors > Home > ILE Home > Th. List > df-rsqrt | Unicode version |
Description: Define a function whose
value is the square root of a nonnegative real
number.
Defining the square root for complex numbers has one difficult part: choosing between the two roots. The usual way to define a principal square root for all complex numbers relies on excluded middle or something similar. But in the case of a nonnegative real number, we don't have the complications presented for general complex numbers, and we can choose the nonnegative root. (Contributed by Jim Kingdon, 23-Aug-2020.) |
Ref | Expression |
---|---|
df-rsqrt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csqrt 10960 | . 2 | |
2 | vx | . . 3 | |
3 | cr 7773 | . . 3 | |
4 | vy | . . . . . . . 8 | |
5 | 4 | cv 1347 | . . . . . . 7 |
6 | c2 8929 | . . . . . . 7 | |
7 | cexp 10475 | . . . . . . 7 | |
8 | 5, 6, 7 | co 5853 | . . . . . 6 |
9 | 2 | cv 1347 | . . . . . 6 |
10 | 8, 9 | wceq 1348 | . . . . 5 |
11 | cc0 7774 | . . . . . 6 | |
12 | cle 7955 | . . . . . 6 | |
13 | 11, 5, 12 | wbr 3989 | . . . . 5 |
14 | 10, 13 | wa 103 | . . . 4 |
15 | 14, 4, 3 | crio 5808 | . . 3 |
16 | 2, 3, 15 | cmpt 4050 | . 2 |
17 | 1, 16 | wceq 1348 | 1 |
Colors of variables: wff set class |
This definition is referenced by: sqrtrval 10964 absval 10965 |
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