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Theorems · Theorem · order theory

le_smul_ceilDiv

∀ {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 : CeilDiv α β] {a : α} {b : β},
  0 < a → b ≤ a • (b ⌈/⌉ a)
Defined in
Mathlib.Algebra.Order.Floor.Div
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
AddCommMonoidPartialOrderAddCommMonoidPartialOrderSMulZeroClassCeilDiv
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Around this declaration

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

floorDiv_le_ceilDiv · cited by 0floorDiv_le_ceilDivAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderle_rfl · cited by 1558le_rflSMulZeroClass · cited by 213SMulZeroClassCeilDiv.ceilDiv · cited by 25CeilDiv.ceilDivCeilDiv · cited by 20CeilDivceilDiv_le_iff_le_smul · cited by 3ceilDiv_le_iff_le_smulle_smul_ceilDivCITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.