Theorems · Theorem · order theory
pow_unbounded_of_one_lt
∀ {R : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [IsStrictOrderedRing R] [Archimedean R] {y : R}
[ExistsAddOfLE R] (x : R), 1 < y → ∃ n, x < y ^ n- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- add_commproof · cited by 1,535
- Archimedeanstatement and proof · cited by 603
- ExistsAddOfLEstatement and proof · cited by 330
- exists_pos_add_of_lt'proof · cited by 5
- add_one_pow_unbounded_of_posproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- exists_pow_lt_of_lt_oneproof · cited by 16
- NormedField.exists_lt_normproof · cited by 14
- exists_mem_Ico_zpowproof · cited by 3
- tendsto_pow_atTop_nhds_zero_iffproof · cited by 2
- exists_nat_pow_nearproof · cited by 2
- Liouville.transcendentalproof · cited by 1