Definition df-lfig 43853

Description: Define the class of finitely generated left modules. Finite generation of subspaces can be interpreted 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 43852	. 2 class LFinGen
2		vw	. . . . . 6 setvar 𝑤
3	2	cv 1569	. . . . 5 class 𝑤
4		cbs 17291	. . . . 5 class Base
5	3, 4	cfv 6540	. . . 4 class (Base‘𝑤)
6		clspn 21142	. . . . . 6 class LSpan
7	3, 6	cfv 6540	. . . . 5 class (LSpan‘𝑤)
8	5	cpw 4564	. . . . . 6 class 𝒫 (Base‘𝑤)
9		cfn 8949	. . . . . 6 class Fin
10	8, 9	cin 3905	. . . . 5 class (𝒫 (Base‘𝑤) ∩ Fin)
11	7, 10	cima 5666	. . . 4 class ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))
12	5, 11	wcel 2146	. . 3 wff (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))
13		clmod 21031	. . 3 class LMod
14	12, 2, 13	crab 3418	. 2 class {𝑤 ∈ LMod ∣ (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))}
15	1, 14	wceq 1570	1 wff LFinGen = {𝑤 ∈ LMod ∣ (Base‘𝑤) ∈ ((LSpan‘𝑤) “ (𝒫 (Base‘𝑤) ∩ Fin))}

This definition is used by:  islmodfg  43854  fglmod  43858