Theorems · Theorem · commutative algebra
ValuativeRel.vlt.trans_vle
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y z : R}, x <ᵥ y → y ≤ᵥ z → x <ᵥ zAlias of ValuativeRel.vlt_of_vlt_of_vle.
- 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.vltstatement · cited by 49
- ValuativeRel.vlt_of_vlt_of_vleproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ValuativeRel.vlt.transproof · cited by 0
- ValuativeRel.mul_vlt_mul_of_vle_of_vltproof · cited by 0
- ValuativeRel.vlt_of_vlt_of_veqproof · cited by 0
- ValuativeRel.vlt_imp_vlt_of_vle_of_vleproof · cited by 0