Theorems · Theorem · order theory
sub_toIcoDiv_zsmul_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), b - toIcoDiv hp a b • p ∈ Set.Ico a (a + p)- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 6 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.
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
- toIcoDivstatement · cited by 84
- existsUnique_sub_zsmul_mem_Icoproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- toIcoMod_mem_Icoproof · cited by 9
- toIcoDiv_add_zsmulproof · cited by 6
- toIcoDiv_add_zsmul'proof · cited by 5
- toIcoDiv_sub_eq_toIcoDiv_addproof · cited by 3
- toIcoDiv_negproof · cited by 3
- iUnion_Ico_add_zsmulproof · cited by 2