Theorems · Theorem · number theory
ZLattice.normBound_pos
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
{L : Submodule ℤ E} [inst_3 : DiscreteTopology ↥L] {ι : Type u_3} (b : Module.Basis ι ℤ ↥L), 0 < ZLattice.normBound b- Defined in
- Mathlib.Algebra.Module.ZLattice.Summable
- Cited by
- 4 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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Submodulestatement and proof · cited by 7,192
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.Basisstatement and proof · cited by 1,477
- DiscreteTopologystatement and proof · cited by 373
- ZLattice.normBoundstatement · cited by 8
- ZLattice.exists_forall_abs_repr_le_normproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ZLattice.exists_finsetSum_norm_rpow_le_tsumproof · cited by 2
- ZLattice.abs_repr_leproof · cited by 1
- ZLattice.abs_repr_lt_of_norm_ltproof · cited by 1
- ZLattice.sum_piFinset_Icc_rpow_leproof · cited by 1