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Theorems · Theorem · order theory

smul_floorDiv_le

∀ {α : Type u_2} {β : Type u_3} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : AddCommMonoid β]
  [inst_3 : PartialOrder β] [inst_4 : SMulZeroClass α β] [inst_5 : FloorDiv α β] {a : α} {b : β},
  0 < a → a • (b ⌊/⌋ a) ≤ b
Defined in
Mathlib.Algebra.Order.Floor.Div
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
AddCommMonoidPartialOrderAddCommMonoidPartialOrderSMulZeroClassFloorDiv
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Around this declaration

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

Nat.factorization_floorRoot · cited by 1Nat.factorization_floorRo…floorDiv_le_ceilDiv · cited by 0floorDiv_le_ceilDivAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderle_rfl · cited by 1558le_rflSMulZeroClass · cited by 213SMulZeroClassFloorDiv.floorDiv · cited by 24FloorDiv.floorDivFloorDiv · cited by 20FloorDivle_floorDiv_iff_smul_le · cited by 3le_floorDiv_iff_smul_lesmul_floorDiv_leCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.