Theorems · Definition · commutative algebra
ValuativeRel.veq
{R : Type u_1} → [inst : Semiring R] → [ValuativeRel R] → R → R → PropThe valuation equals relation, defined as x =ᵥ y ↔ x ≤ᵥ y ∧ y ≤ᵥ x.
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- SemiringValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- ValuativeRelstatement and proof · cited by 241
- AntisymmRelproof · cited by 93
- ValuativeRel.vleproof · cited by 84
Cited by27
Results whose statement or proof uses this declaration.
- ValuativeRel.veq_mul_commstatement · cited by 4
- ValuativeRel.veq_reflstatement · cited by 4
- ValuativeRel.veq.vlestatement · cited by 4
- ValuativeRel.veq_commstatement · cited by 2
- ValuativeRel.veq.symmstatement · cited by 2
- ValuativeRel.veq.vgestatement · cited by 2
- ValuativeRel.mul_veq_mulstatement and proof · cited by 2
- ValuativeRel.veq_mul_right_commstatement and proof · cited by 1
- ValuativeRel.veq_rflstatement · cited by 1
- ValuativeRel.vge_of_veqstatement and proof · cited by 1
- ValuativeRel.vle_of_veqstatement and proof · cited by 1
- ValuativeRel.zero_veq_iffstatement and proof · cited by 1