Theorems · Theorem · number theory

Module.Basis.ofZLatticeBasis_span

∀ (K : Type u_1) [inst : NormedField K] [inst_1 : LinearOrder K] [inst_2 : IsStrictOrderedRing K]
  [inst_3 : HasSolidNorm K] [inst_4 : FloorRing K] {E : Type u_2} [inst_5 : NormedAddCommGroup E]
  [inst_6 : NormedSpace K E] [inst_7 : FiniteDimensional K E] [inst_8 : ProperSpace E] (L : Submodule ℤ E)
  [inst_9 : DiscreteTopology ↥L] {ι : Type u_3} [hs : IsZLattice K L] (b : Module.Basis ι ℤ ↥L),
  Submodule.span ℤ (Set.range ⇑(Module.Basis.ofZLatticeBasis K L b)) = L

Defined in

Mathlib.Algebra.Module.ZLattice.Basic

Cited by

6 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldLinearOrderIsStrictOrderedRingHasSolidNormFloorRingNormedAddCommGroupNormedSpaceFiniteDimensionalProperSpaceDiscreteTopologyIsZLattice