Theorems · Theorem · order theory
ceilDiv_le_iff_le_smul
∀ {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 c : β},
0 < a → (b ⌈/⌉ a ≤ c ↔ b ≤ a • c)- Defined in
- Mathlib.Algebra.Order.Floor.Div
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 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
- gc_smul_ceilDivproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Nat.dvd_pow_iff_ceilRoot_dvdproof · cited by 1
- le_smul_ceilDivproof · cited by 1
- ceilDiv_le_iff_le_mulproof · cited by 0