Theorems · Theorem · order theory
toIcoDiv_sub_eq_toIcoDiv_add
∀ {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 c : α), toIcoDiv hp a (b - c) = toIcoDiv hp (a + c) b- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.Icoproof · cited by 799
- Archimedeanstatement and proof · cited by 603
- add_right_commproof · cited by 85
- toIcoDivstatement and proof · cited by 84
- sub_right_commproof · cited by 15
- toIcoDiv_eq_of_sub_zsmul_mem_Icoproof · cited by 7
- sub_toIcoDiv_zsmul_mem_Icoproof · cited by 6
- Set.sub_mem_Ico_iff_leftproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- toIcoMod_sub_eq_subproof · cited by 2
- toIcoDiv_sub_eq_toIcoDiv_add'proof · cited by 1
- toIcoDiv_eq_subproof · cited by 0