Theorems · Theorem · commutative algebra
ValuativeRel.veq.vle
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y : R}, x =ᵥ y → x ≤ᵥ yAlias of ValuativeRel.vle_of_veq.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- SemiringValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- ValuativeRelstatement · cited by 241
- ValuativeRel.vlestatement · cited by 84
- ValuativeRel.veqstatement · cited by 27
- ValuativeRel.vle_of_veqproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ValuativeRel.mul_veq_mulproof · cited by 2
- ValuativeRel.not_vgt_of_veqproof · cited by 1
- ValuativeRel.vlt_of_veq_of_vltproof · cited by 0
- ValuativeRel.vlt_of_vlt_of_veqproof · cited by 0