Theorems · Theorem · order theory
toIocMod_mem_Ioc
∀ {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 ∈ Set.Ioc a (a + p)- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- toIocModstatement · cited by 109
- sub_toIocDiv_zsmul_mem_Iocproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- toIocMod_eq_iffproof · cited by 4
- Complex.arg_expproof · cited by 3
- Complex.norm_eq_one_iff'proof · cited by 2
- toIocMod_le_rightproof · cited by 1
- left_lt_toIocModproof · cited by 1
- QuotientAddGroup.equivIocMod_coestatement · cited by 0
- QuotientAddGroup.equivIocMod_zerostatement · cited by 0
- AddCircle.equivIccQuot_comp_mk_eq_toIocModstatement and proof · cited by 0