Theorems · Theorem · order theory
existsUnique_add_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
- 7 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- add_assocproof · cited by 746
- Archimedeanstatement and proof · cited by 603
- ExistsUniquestatement and proof · cited by 268
- Equiv.bijectiveproof · cited by 132
- add_le_add_iff_rightproof · cited by 47
- Equiv.addRightproof · cited by 30
- sub_lt_iff_lt_add'proof · cited by 30
Cited by7
Results whose statement or proof uses this declaration.
- Complex.arg_mem_Iocproof · cited by 6
- Complex.exp_eq_one_iffproof · cited by 3
- existsUnique_sub_zsmul_mem_Iocproof · cited by 3
- AddSubgroup.dense_of_not_isolated_zeroproof · cited by 2
- isAddFundamentalDomain_Ioc'proof · cited by 2
- Function.Periodic.exists_mem_Iocproof · cited by 1
- isAddFundamentalDomain_Iocproof · cited by 1