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Theorems · Theorem · number theory

IsZLattice.span_top

∀ {K : Type u_1} {inst : NormedField K} {E : Type u_2} {inst_1 : NormedAddCommGroup E} {inst_2 : NormedSpace K E}
  {L : Submodule ℤ E} {inst_3 : DiscreteTopology ↥L} [self : IsZLattice K L], Submodule.span K ↑L = ⊤

L spans the full space E over K.

Defined in
Mathlib.Algebra.Module.ZLattice.Basic
Cited by
2 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IsZLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ZLattice.rank · cited by 5ZLattice.rankZLattice.FG · cited by 1ZLattice.FGNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceTop.top · cited by 9680Top.topSetLike.coe · cited by 8199SetLike.coeSubmodule · cited by 7192SubmoduleSubmodule.span · cited by 1504Submodule.spanNormedField · cited by 1084NormedFieldDiscreteTopology · cited by 373DiscreteTopologyIsZLattice · cited by 32IsZLatticeIsZLattice.span_topCITED BYCITES

Cites9

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Cited by2

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