Theorems · Theorem · commutative algebra
Valuation.IsEquiv.lt_one_iff_lt_one
∀ {R : Type u_3} {Γ₀ : Type u_4} {Γ'₀ : Type u_5} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀]
[inst_2 : LinearOrderedCommMonoidWithZero Γ'₀] {v₁ : Valuation R Γ₀} {v₂ : Valuation R Γ'₀},
v₁.IsEquiv v₂ → ∀ {x : R}, v₁ x < 1 ↔ v₂ x < 1- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
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.
- DFunLike.coestatement and proof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- map_oneproof · cited by 861
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.IsEquivstatement and proof · cited by 67
- Valuation.map_oneproof · cited by 17
- Valuation.IsEquiv.lt_iff_ltproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Valuation.isEquiv_iff_val_lt_oneproof · cited by 3
- Padic.valuation_p_lt_oneproof · cited by 0