Theorems · Theorem · number theory

ZLattice.normBound_spec

∀ {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) (x : ↥L) (i : ι),
  ZLattice.normBound b * ↑|(b.repr x) i| ≤ ‖x‖

Defined in

Mathlib.Algebra.Module.ZLattice.Summable

Cited by

1 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceFiniteDimensionalDiscreteTopology