Theorems · Theorem · number theory

ZSpan.coe_floor_self

∀ {ι : Type u_2} {K : Type u_3} [inst : NormedField K] [inst_1 : LinearOrder K] [inst_2 : IsStrictOrderedRing K]
  [inst_3 : FloorRing K] [inst_4 : Fintype ι] [inst_5 : Unique ι] (k : K),
  ↑(ZSpan.floor (Module.Basis.singleton ι K) k) = ↑⌊k⌋

Defined in: Mathlib.Algebra.Module.ZLattice.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField LinearOrder IsStrictOrderedRing FloorRing Fintype Unique

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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
LinearOrderstatement and proof · cited by 8,572
Fintypestatement and proof · cited by 7,736
Submodulestatement · cited by 7,192
Set.rangestatement · cited by 4,705
IsStrictOrderedRingstatement and proof · cited by 2,490
Submodule.spanstatement · cited by 1,504
Module.Basisstatement · cited by 1,477
NormedFieldstatement and proof · cited by 1,084
Module.Basis.reprproof · cited by 498
FloorRingstatement and proof · cited by 405
Uniquestatement and proof · cited by 400

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