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Mirrors > Home > HSE Home > Th. List > df-nlfn | Structured version Visualization version GIF version |
Description: Define the null space of a Hilbert space functional. (Contributed by NM, 11-Feb-2006.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-nlfn | ⊢ null = (𝑡 ∈ (ℂ ↑m ℋ) ↦ (◡𝑡 “ {0})) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnl 29936 | . 2 class null | |
2 | vt | . . 3 setvar 𝑡 | |
3 | cc 11054 | . . . 4 class ℂ | |
4 | chba 29903 | . . . 4 class ℋ | |
5 | cmap 8768 | . . . 4 class ↑m | |
6 | 3, 4, 5 | co 7358 | . . 3 class (ℂ ↑m ℋ) |
7 | 2 | cv 1541 | . . . . 5 class 𝑡 |
8 | 7 | ccnv 5633 | . . . 4 class ◡𝑡 |
9 | cc0 11056 | . . . . 5 class 0 | |
10 | 9 | csn 4587 | . . . 4 class {0} |
11 | 8, 10 | cima 5637 | . . 3 class (◡𝑡 “ {0}) |
12 | 2, 6, 11 | cmpt 5189 | . 2 class (𝑡 ∈ (ℂ ↑m ℋ) ↦ (◡𝑡 “ {0})) |
13 | 1, 12 | wceq 1542 | 1 wff null = (𝑡 ∈ (ℂ ↑m ℋ) ↦ (◡𝑡 “ {0})) |
Colors of variables: wff setvar class |
This definition is referenced by: nlfnval 30865 |
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