Theorems · Theorem · order theory
left_lt_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 < toIocMod hp a b- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 1 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.
Cites7
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
- Set.mem_Iocproof · cited by 20
- toIocMod_mem_Iocproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Real.Angle.neg_pi_lt_toRealproof · cited by 4