Theorems · Theorem · number theory

ZSpan.norm_fract_le

∀ {E : Type u_1} {ι : Type u_2} {K : Type u_3} [inst : NormedField K] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace K E] (b : Module.Basis ι K E) [inst_3 : LinearOrder K] [inst_4 : IsStrictOrderedRing K]
  [inst_5 : FloorRing K] [inst_6 : Fintype ι] [HasSolidNorm K] (m : E), ‖ZSpan.fract b m‖ ≤ ∑ i, ‖b i‖

Defined in

Mathlib.Algebra.Module.ZLattice.Basic

Cited by

2 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedAddCommGroupNormedSpaceLinearOrderIsStrictOrderedRingFloorRingFintypeHasSolidNorm