Theorems · Theorem · linear algebra
Submodule.coe_iSup_of_chain
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(a : ℕ →o Submodule R M), ↑(⨆ k, a k) = ⋃ k, ↑(a k)- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- OrderHomstatement and proof · cited by 934
- OrderHom.monotoneproof · cited by 70
- Monotone.directed_leproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.coe_scott_continuousproof · cited by 0