Theorems · Theorem · order theory
toIocMod_sub_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 = -toIocDiv hp a b • p- 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.
Cites8
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
- Archimedeanstatement and proof · cited by 603
- neg_smulproof · cited by 306
- toIocModstatement · cited by 109
- toIocDivstatement and proof · cited by 85
- sub_sub_cancel_leftproof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- Real.Angle.coe_toIocModproof · cited by 2
- Complex.arg_mul_cos_add_sin_mul_I_subproof · cited by 1
- toIocMod_sub_self_eq_mulproof · cited by 0