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Definition df-lsp 19020
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 19019 . 2 class LSpan
2 vw . . 3 setvar 𝑤
3 cvv 3231 . . 3 class V
4 vs . . . 4 setvar 𝑠
52cv 1522 . . . . . 6 class 𝑤
6 cbs 15904 . . . . . 6 class Base
75, 6cfv 5926 . . . . 5 class (Base‘𝑤)
87cpw 4191 . . . 4 class 𝒫 (Base‘𝑤)
94cv 1522 . . . . . . 7 class 𝑠
10 vt . . . . . . . 8 setvar 𝑡
1110cv 1522 . . . . . . 7 class 𝑡
129, 11wss 3607 . . . . . 6 wff 𝑠𝑡
13 clss 18980 . . . . . . 7 class LSubSp
145, 13cfv 5926 . . . . . 6 class (LSubSp‘𝑤)
1512, 10, 14crab 2945 . . . . 5 class {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}
1615cint 4507 . . . 4 class {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}
174, 8, 16cmpt 4762 . . 3 class (𝑠 ∈ 𝒫 (Base‘𝑤) ↦ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡})
182, 3, 17cmpt 4762 . 2 class (𝑤 ∈ V ↦ (𝑠 ∈ 𝒫 (Base‘𝑤) ↦ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠𝑡}))
191, 18wceq 1523 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  19021
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