Theorems · Theorem · order theory
existsUnique_add_zpow_mem_Ioc
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] [MulArchimedean G] {a : G},
1 < a → ∀ (b c : G), ∃! m, b * a ^ m ∈ Set.Ioc c (c * a)- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 2 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- CommGroupstatement and proof · cited by 990
- Set.Iocstatement and proof · cited by 971
- IsOrderedMonoidstatement and proof · cited by 577
- ExistsUniquestatement and proof · cited by 268
- Equiv.bijectiveproof · cited by 132
- MulArchimedeanstatement and proof · cited by 45
- Equiv.addRightproof · cited by 30
- zpow_add_oneproof · cited by 18
- Function.Bijective.existsUnique_iffproof · cited by 8
- existsUnique_zpow_near_of_one_ltproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.dense_of_not_isolated_oneproof · cited by 2
- existsUnique_sub_zpow_mem_Iocproof · cited by 0