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Definition df-span 28508
Description: Define the linear span of a subset of Hilbert space. Definition of span in [Schechter] p. 276. See spanval 28532 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 28129 . 2 class span
2 vx . . 3 setvar 𝑥
3 chil 28116 . . . 4 class
43cpw 4297 . . 3 class 𝒫 ℋ
52cv 1630 . . . . . 6 class 𝑥
6 vy . . . . . . 7 setvar 𝑦
76cv 1630 . . . . . 6 class 𝑦
85, 7wss 3723 . . . . 5 wff 𝑥𝑦
9 csh 28125 . . . . 5 class S
108, 6, 9crab 3065 . . . 4 class {𝑦S𝑥𝑦}
1110cint 4611 . . 3 class {𝑦S𝑥𝑦}
122, 4, 11cmpt 4863 . 2 class (𝑥 ∈ 𝒫 ℋ ↦ {𝑦S𝑥𝑦})
131, 12wceq 1631 1 wff span = (𝑥 ∈ 𝒫 ℋ ↦ {𝑦S𝑥𝑦})
Colors of variables: wff setvar class
This definition is referenced by:  spanval  28532
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