Theorems · Theorem · order theory
toIocDiv_eq_iff
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [inst_2 : IsOrderedAddMonoid α] [hα : Archimedean α]
{p : α} (hp : 0 < p) {a b : α} {n : ℤ}, toIocDiv hp a b = n ↔ b - n • p ∈ Set.Ioc a (a + p)- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.Iocstatement · cited by 971
- Archimedeanstatement and proof · cited by 603
- toIocDivstatement · cited by 85
- existsUnique_sub_zsmul_mem_Iocproof · cited by 3
- ExistsUnique.choose_eq_iffproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- toIocDiv_eq_of_sub_zsmul_mem_Iocproof · cited by 8
- eventuallyEq_toIocDiv_nhdsLEproof · cited by 2
- eventuallyEq_toIcoDiv_nhdsLTproof · cited by 1