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Definition df-lsp 18741
Description: Define span of a set of vectors of a left module or left vector space. (Contributed by NM, 8-Dec-2013.)
Assertion
Ref Expression
df-lsp LSpan = (𝑤 ∈ V ↦ (𝑠 ∈ 𝒫 (Base‘𝑤) ↦ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}))
Distinct variable group:   𝑤,𝑠,𝑡

Detailed syntax breakdown of Definition df-lsp
StepHypRef Expression
1 clspn 18740 . 2 class LSpan
2 vw . . 3 setvar 𝑤
3 cvv 3172 . . 3 class V
4 vs . . . 4 setvar 𝑠
52cv 1473 . . . . . 6 class 𝑤
6 cbs 15643 . . . . . 6 class Base
75, 6cfv 5789 . . . . 5 class (Base‘𝑤)
87cpw 4107 . . . 4 class 𝒫 (Base‘𝑤)
94cv 1473 . . . . . . 7 class 𝑠
10 vt . . . . . . . 8 setvar 𝑡
1110cv 1473 . . . . . . 7 class 𝑡
129, 11wss 3539 . . . . . 6 wff 𝑠𝑡
13 clss 18701 . . . . . . 7 class LSubSp
145, 13cfv 5789 . . . . . 6 class (LSubSp‘𝑤)
1512, 10, 14crab 2899 . . . . 5 class {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}
1615cint 4404 . . . 4 class {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}
174, 8, 16cmpt 4637 . . 3 class (𝑠 ∈ 𝒫 (Base‘𝑤) ↦ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡})
182, 3, 17cmpt 4637 . 2 class (𝑤 ∈ V ↦ (𝑠 ∈ 𝒫 (Base‘𝑤) ↦ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}))
191, 18wceq 1474 1 wff LSpan = (𝑤 ∈ V ↦ (𝑠 ∈ 𝒫 (Base‘𝑤) ↦ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}))
Colors of variables: wff setvar class
This definition is referenced by:  lspfval  18742
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