Theorems · Theorem · general topology
continuum_le_cardinal_of_module
∀ (𝕜 : Type u) (E : Type v) [inst : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜] [inst_2 : AddCommGroup E] [Module 𝕜 E] [Nontrivial E], Cardinal.continuum ≤ Cardinal.mk E
A nontrivial module over a complete nontrivially normed field has cardinality at least continuum.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- LE.le.transproof · cited by 3,151
- Cardinalstatement · cited by 2,598
- CompleteSpacestatement and proof · cited by 2,532
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.continuumstatement and proof · cited by 60
- Cardinal.lift_continuumproof · cited by 7
- continuum_le_cardinal_of_nontriviallyNormedFieldproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- continuum_le_cardinal_of_isOpenproof · cited by 1