Theorems · Theorem · order theory
AddCommGroup.not_modEq_iff_toIcoMod_eq_toIocMod
∀ {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}, ¬a ≡ b [PMOD p] ↔ toIcoMod hp a b = toIocMod hp a b- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- toIocModstatement · cited by 109
- AddCommGroup.ModEqstatement · cited by 107
- toIcoModstatement · cited by 99
- Iff.not_leftproof · cited by 49
- AddCommGroup.modEq_iff_toIcoMod_ne_toIocModproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AddCommGroup.not_modEq_iff_toIcoDiv_eq_toIocDivproof · cited by 3
- AddCircle.equivIccQuot_comp_mk_eq_toIocModproof · cited by 0
- toIcoMod_eventuallyEq_toIocModproof · cited by 0