Theorems · Theorem · linear algebra
Submodule.finite_span_isCompactElement
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (S : Set M),
S.Finite → IsCompactElement (Submodule.span R S)The span of a finite subset is compact in the lattice of submodules.
- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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- Setstatement and proof · 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
- Submodulestatement · cited by 7,192
- Set.Finitestatement and proof · cited by 1,814
- Submodule.spanstatement · cited by 1,504
- Set.Finite.toFinsetproof · cited by 351
- Set.Finite.coe_toFinsetproof · cited by 124
- IsCompactElementstatement · cited by 34
- Submodule.finset_span_isCompactElementproof · cited by 1
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