Theorems · Theorem · order theory
MulArchimedean.arch
∀ {R : Type u_2} {inst : CommMonoid R} {inst_1 : PartialOrder R} [self : MulArchimedean R] (x : R) {y : R},
1 < y → ∃ n, x ≤ y ^ nFor any two elements x, y such that 1 < y, there exists a natural number n
such that x ≤ y ^ n.
- Defined in
- Mathlib.Algebra.Order.Archimedean.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MulArchimedean
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- CommMonoidstatement and proof · cited by 2,264
- MulArchimedeanstatement and proof · cited by 45
Cited by5
Results whose statement or proof uses this declaration.
- MulArchimedean.comapproof · cited by 5
- existsUnique_zpow_near_of_one_ltproof · cited by 3
- OrderMonoidIso.mulArchimedeanproof · cited by 2
- exists_lt_powproof · cited by 1
- MulArchimedeanClass.mk_eq_mk_of_mulArchimedeanproof · cited by 0