Theorems · Theorem · commutative algebra
Valuation.Compatible.vle_iff_le
∀ {R : Type u_1} {Γ : Type u_2} {inst : Ring R} {inst_1 : LinearOrderedCommMonoidWithZero Γ} {v : Valuation R Γ}
{inst_2 : ValuativeRel R} [self : v.Compatible] (x y : R), x ≤ᵥ y ↔ v x ≤ v y- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
- Assumes
- Valuation.Compatible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Valuationstatement and proof · cited by 823
- ValuativeRelstatement and proof · cited by 241
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- ValuativeRel.vlestatement · cited by 84
- Valuation.Compatiblestatement and proof · cited by 71
Cited by3
Results whose statement or proof uses this declaration.
- Valuation.vle_iff_leproof · cited by 3
- ValuativeRel.isNontrivial_iff_isNontrivialproof · cited by 1
- ValuativeRel.eq_trivialRel_of_compatible_oneproof · cited by 1