Definition df-lfig 42112

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

Step	Hyp	Ref	Expression
1		clfig 42111	. 2 class LFinGen
2		vw	. . . . . 6 setvar 𝑤
3	2	cv 1538	. . . . 5 class 𝑤
4		cbs 17148	. . . . 5 class Base
5	3, 4	cfv 6542	. . . 4 class (Base‘𝑤)
6		clspn 20726	. . . . . 6 class LSpan
7	3, 6	cfv 6542	. . . . 5 class (LSpan‘𝑤)
8	5	cpw 4601	. . . . . 6 class 𝒫 (Base‘𝑤)
9		cfn 8941	. . . . . 6 class Fin
10	8, 9	cin 3946	. . . . 5 class (𝒫 (Base‘𝑤) ∩ Fin)
11	7, 10	cima 5678	. . . 4 class ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))
12	5, 11	wcel 2104	. . 3 wff (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))
13		clmod 20614	. . 3 class LMod
14	12, 2, 13	crab 3430	. 2 class {𝑤 ∈ LMod ∣ (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))}
15	1, 14	wceq 1539	1 wff LFinGen = {𝑤 ∈ LMod ∣ (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))}

This definition is referenced by:  islmodfg  42113  fglmod  42117