HSE Home Hilbert Space Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HSE Home  >  Th. List  >  df-span Structured version   Visualization version   GIF version

Definition df-span 27334
Description: Define the linear span of a subset of Hilbert space. Definition of span in [Schechter] p. 276. See spanval 27358 for its value. (Contributed by NM, 2-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
df-span span = (𝑥 ∈ 𝒫 ℋ ↦ {𝑦S𝑥𝑦})
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-span
StepHypRef Expression
1 cspn 26955 . 2 class span
2 vx . . 3 setvar 𝑥
3 chil 26942 . . . 4 class
43cpw 4011 . . 3 class 𝒫 ℋ
52cv 1473 . . . . . 6 class 𝑥
6 vy . . . . . . 7 setvar 𝑦
76cv 1473 . . . . . 6 class 𝑦
85, 7wss 3444 . . . . 5 wff 𝑥𝑦
9 csh 26951 . . . . 5 class S
108, 6, 9crab 2804 . . . 4 class {𝑦S𝑥𝑦}
1110cint 4308 . . 3 class {𝑦S𝑥𝑦}
122, 4, 11cmpt 4541 . 2 class (𝑥 ∈ 𝒫 ℋ ↦ {𝑦S𝑥𝑦})
131, 12wceq 1474 1 wff span = (𝑥 ∈ 𝒫 ℋ ↦ {𝑦S𝑥𝑦})
Colors of variables: wff setvar class
This definition is referenced by:  spanval  27358
  Copyright terms: Public domain W3C validator