Theorems · Theorem · commutative algebra
ValuativeRel.vle.trans
∀ {R : Type u_1} {inst : Semiring R} [self : ValuativeRel R] {z y x : R}, x ≤ᵥ y → y ≤ᵥ z → x ≤ᵥ zAlias of ValuativeRel.vle_trans.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- ValuativeRel
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 · cited by 13,802
- ValuativeRelstatement · cited by 241
- ValuativeRel.vlestatement · cited by 84
- ValuativeRel.vle_transproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- ValuativeRel.mul_vle_mulproof · cited by 2
- ValuativeRel.vle_trans'proof · cited by 1
- ValuativeRel.vle_of_veq_of_vleproof · cited by 0
- ValuativeRel.vle_of_vle_of_veqproof · cited by 0