Theorems · Theorem · order theory
Set.sub_mem_Ioc_iff_left
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a b c d : α},
a - b ∈ Set.Ioc c d ↔ a ∈ Set.Ioc (c + b) (d + b)- Defined in
- Mathlib.Algebra.Order.Interval.Set.Group
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 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.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.Iocstatement · cited by 971
- sub_le_iff_le_addproof · cited by 50
- lt_sub_iff_add_ltproof · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- toIocDiv_sub_eq_toIocDiv_addproof · cited by 3
- eventuallyEq_toIocDiv_nhdsLEproof · cited by 2
- eventuallyEq_toIcoDiv_nhdsLTproof · cited by 1