Theorems · Theorem · number theory

ZSpan.smul

∀ {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) {c : K} (hc : c ≠ 0),
  c • Submodule.span ℤ (Set.range ⇑b) = Submodule.span ℤ (Set.range ⇑(b.isUnitSMul ⋯))

Defined in: Mathlib.Algebra.Module.ZLattice.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField NormedAddCommGroup NormedSpace

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

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setproof · cited by 53,352
Moduleproof · cited by 20,661
NormedAddCommGroupstatement and proof · cited by 15,752
Semiringproof · cited by 13,802
NormedSpacestatement and proof · cited by 12,499
AddCommMonoidproof · cited by 12,281
Submodulestatement and proof · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Submodule.spanstatement and proof · cited by 1,504
Module.Basisstatement and proof · cited by 1,477
NormedFieldstatement and proof · cited by 1,084

Cited by2

Results whose statement or proof uses this declaration.

BoxIntegral.unitPartition.mem_smul_span_iffproof · cited by 2
BoxIntegral.unitPartition.integralSum_eq_tsum_divproof · cited by 1