Theorems · Theorem · order theory
toIocMod_eq_self
∀ {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}, toIocMod hp a b = b ↔ b ∈ Set.Ioc a (a + p)- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- add_zeroproof · cited by 2,707
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.Iocstatement and proof · cited by 971
- zero_smulproof · cited by 716
- Archimedeanstatement and proof · cited by 603
- toIocModstatement · cited by 109
- toIocMod_eq_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Real.Angle.toReal_coe_eq_self_iffproof · cited by 11
- Complex.norm_sub_mem_Icc_angleproof · cited by 2