Theorems · Theorem · order theory
toIocMod_eq_iff
∀ {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}, toIocMod hp a b = c ↔ c ∈ Set.Ioc a (a + p) ∧ ∃ z, b = c + z • p- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 56 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.
- 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 and proof · cited by 971
- Archimedeanstatement and proof · cited by 603
- toIocModstatement and proof · cited by 109
- toIocDivproof · cited by 85
- toIocMod_mem_Iocproof · cited by 8
- toIocDiv_eq_of_sub_zsmul_mem_Iocproof · cited by 8
- toIocMod_add_toIocDiv_zsmulproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- AddCommGroup.tfae_modEqproof · cited by 3
- toIocMod_eq_selfproof · cited by 2
- toIocMod_apply_leftproof · cited by 1
- toIocMod_apply_rightproof · cited by 0