Theorems · Theorem · order theory
exists_pow_btwn
∀ {K : Type u_4} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] [Archimedean K] {n : ℕ},
n ≠ 0 → ∀ {x y : K}, x < y → 0 < y → ∃ q, 0 < q ∧ x < q ^ n ∧ q ^ n < y- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- absproof · cited by 1,814
- MulZeroClass.zero_mulproof · cited by 1,625
- LT.lt.ne'proof · cited by 1,417
Cited by1
Results whose statement or proof uses this declaration.
- exists_rat_pow_btwnproof · cited by 2