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Definition df-lfig 38159
Description: Define the class of finitely generated left modules. Finite generation of subspaces can be intepreted using s. (Contributed by Stefan O'Rear, 1-Jan-2015.)
Assertion
Ref Expression
df-lfig LFinGen = {𝑤 ∈ LMod ∣ (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))}

Detailed syntax breakdown of Definition df-lfig
StepHypRef Expression
1 clfig 38158 . 2 class LFinGen
2 vw . . . . . 6 setvar 𝑤
32cv 1631 . . . . 5 class 𝑤
4 cbs 16080 . . . . 5 class Base
53, 4cfv 6050 . . . 4 class (Base‘𝑤)
6 clspn 19194 . . . . . 6 class LSpan
73, 6cfv 6050 . . . . 5 class (LSpan‘𝑤)
85cpw 4303 . . . . . 6 class 𝒫 (Base‘𝑤)
9 cfn 8124 . . . . . 6 class Fin
108, 9cin 3715 . . . . 5 class (𝒫 (Base‘𝑤) ∩ Fin)
117, 10cima 5270 . . . 4 class ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))
125, 11wcel 2140 . . 3 wff (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))
13 clmod 19086 . . 3 class LMod
1412, 2, 13crab 3055 . 2 class {𝑤 ∈ LMod ∣ (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))}
151, 14wceq 1632 1 wff LFinGen = {𝑤 ∈ LMod ∣ (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))}
Colors of variables: wff setvar class
This definition is referenced by:  islmodfg  38160  fglmod  38164
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