Theorems · Theorem · order theory
add_one_pow_unbounded_of_pos
∀ {R : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [IsStrictOrderedRing R] [Archimedean R] {y : R} (x : R),
0 < y → ∃ n, x < (y + 1) ^ n- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 31 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.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.leproof · cited by 2,189
- add_commproof · cited by 1,535
- Archimedeanstatement and proof · cited by 603
- nsmul_eq_mulproof · cited by 369
- zero_le_oneproof · cited by 316
- pow_nonnegproof · cited by 141
- add_nonnegproof · cited by 104
- zero_le_twoproof · cited by 44
- Archimedean.archproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- pow_unbounded_of_one_ltproof · cited by 7
- tendsto_add_one_pow_atTop_atTop_of_posproof · cited by 1
- NNReal.eventually_pow_one_div_leproof · cited by 1