Theorems · Theorem · order theory
toIcoMod_mem_Ico
∀ {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), toIcoMod hp a b ∈ Set.Ico a (a + p)- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 9 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.Icostatement · cited by 799
- Archimedeanstatement and proof · cited by 603
- toIcoModstatement · cited by 99
- sub_toIcoDiv_zsmul_mem_Icoproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- toIcoMod_eq_iffproof · cited by 4
- AddCommGroup.tfae_modEqproof · cited by 3
- AddCircle.equivIccQuot_comp_mk_eq_toIcoModstatement · cited by 1
- QuotientAddGroup.equivIcoMod_coestatement · cited by 0
- QuotientAddGroup.equivIcoMod_zerostatement · cited by 0
- toIcoMod_lt_rightproof · cited by 0
- left_le_toIcoModproof · cited by 0
- toIcoMod_mem_Ico'proof · cited by 0
- AddCircle.equivIccQuot_comp_mk_eq_toIocModproof · cited by 0