Mathlib Map

Theorems · Theorem · order theory

ceilDiv_of_nonpos

∀ {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}, a ≤ 0 → ∀ (b : β), b ⌈/⌉ a = 0
Defined in
Mathlib.Algebra.Order.Floor.Div
Cited by
3 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
AddCommMonoidPartialOrderAddCommMonoidPartialOrderSMulZeroClassCeilDiv
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Nat.factorization_ceilRoot · cited by 1Nat.factorization_ceilRootceilDiv_zero · cited by 0ceilDiv_zerofloorDiv_le_ceilDiv · cited by 0floorDiv_le_ceilDivAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSMulZeroClass · cited by 213SMulZeroClassCeilDiv.ceilDiv · cited by 25CeilDiv.ceilDivCeilDiv · cited by 20CeilDivCeilDiv.ceilDiv_nonpos · cited by 1CeilDiv.ceilDiv_nonposceilDiv_of_nonposCITED BYCITES

Cites6

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

Cited by3

Results whose statement or proof uses this declaration.