Theorems · Theorem · order theory
zero_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), 0 ⌈/⌉ a = 0- Defined in
- Mathlib.Algebra.Order.Floor.Div
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- SMulZeroClassstatement and proof · cited by 213
- CeilDiv.ceilDivstatement · cited by 25
- CeilDivstatement and proof · cited by 20
- CeilDiv.zero_ceilDivproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Nat.ceilRoot_defproof · cited by 3
- Nat.ceilRoot_ne_zeroproof · cited by 2
- Nat.factorization_ceilRootproof · cited by 1
- Finsupp.support_ceilDiv_subsetproof · cited by 1
- Finsupp.ceilDiv_defstatement · cited by 0