Theorems · Theorem · number theory

ZSpan.vadd_mem_fundamentalDomain

∀ {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] (y : ↥(Submodule.span ℤ (Set.range ⇑b))) (x : E),
  y +ᵥ x ∈ ZSpan.fundamentalDomain b ↔ y = -ZSpan.floor b x

Defined in

Mathlib.Algebra.Module.ZLattice.Basic

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedAddCommGroupNormedSpaceLinearOrderIsStrictOrderedRingFloorRingFintype