Theorems · Theorem · field theory
AbsoluteValue.IsEquiv.lt_one_iff
∀ {R : Type u_1} [inst : Semiring R] {S : Type u_2} [inst_1 : Semiring S] [inst_2 : PartialOrder S]
{v w : AbsoluteValue R S} [IsDomain S] [Nontrivial R], v.IsEquiv w → ∀ {x : R}, v x < 1 ↔ w x < 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- map_oneproof · cited by 861
- AbsoluteValuestatement and proof · cited by 363
- AbsoluteValue.IsEquivstatement and proof · cited by 32
- AbsoluteValue.IsEquiv.lt_iff_ltproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AbsoluteValue.isEquiv_iff_lt_one_iffproof · cited by 3
- AbsoluteValue.IsEquiv.log_div_log_eq_log_div_logproof · cited by 1
- AbsoluteValue.IsEquiv.log_div_log_posproof · cited by 1