Theorems · Theorem · number theory
Real.finrank_eq_int_finrank_of_discrete
∀ {E : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {s : Set E},
DiscreteTopology ↥(Submodule.span ℤ s) → Set.finrank ℝ s = Set.finrank ℤ sAssume that the set s spans over ℤ a discrete set. Then its ℝ-rank is equal to its ℤ-rank.
- Defined in
- Mathlib.Algebra.Module.ZLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Submodulestatement and proof · cited by 7,192
- LinearEquivproof · cited by 3,317
- LE.le.transproof · cited by 3,151
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- Submodule.spanstatement and proof · cited by 1,504
- LinearEquiv.symmproof · cited by 1,461
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1