Theorems · Theorem · order theory
existsUnique_sub_zsmul_mem_Ioc
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] [Archimedean G] {a : G},
0 < a → ∀ (b c : G), ∃! m, b - m • a ∈ Set.Ioc c (c + a)- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- ExistsUniquestatement and proof · cited by 268
- sub_neg_eq_addproof · cited by 264
- Equiv.bijectiveproof · cited by 132
- Equiv.negproof · cited by 53
- neg_zsmulproof · cited by 41
- Equiv.neg_applyproof · cited by 34
Cited by4
Results whose statement or proof uses this declaration.
- toIocDivproof · cited by 85
- sub_toIocDiv_zsmul_mem_Iocproof · cited by 5
- toIocDiv_eq_iffproof · cited by 3
- AddConstMapClass.rel_map_of_Iccproof · cited by 2