Theorems · Definition · number theory
IsZLattice.basis
{ι : Type u_1} →
[inst : Fintype ι] →
(L : Submodule ℤ (ι → ℝ)) → [inst_1 : DiscreteTopology ↥L] → [IsZLattice ℝ L] → Module.Basis ι ℤ ↥LReturn an arbitrary ℤ-basis of a lattice L of ι → ℝ indexed by ι.
- Defined in
- Mathlib.Algebra.Module.ZLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Module.Basisstatement · cited by 1,477
- DiscreteTopologystatement and proof · cited by 373
- Module.Free.chooseBasisproof · cited by 121
- Module.Basis.reindexproof · cited by 57
- IsZLatticestatement and proof · cited by 32
- Fintype.equivOfCardEqproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- ZLattice.covolume_div_covolume_eq_relIndexproof · cited by 2