Theorems · Theorem · commutative algebra
ValuativeRel.mul_vlt_mul_of_vlt_of_vle
∀ {R : Type u_2} [inst : Ring R] [inst_1 : ValuativeRel R] {a b c d : R}, a <ᵥ b → c ≤ᵥ d → 0 <ᵥ d → a * c <ᵥ b * d- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
- Assumes
- RingValuativeRel
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.
- Ringstatement and proof · cited by 7,463
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.vlestatement and proof · cited by 84
- ValuativeRel.vltstatement and proof · cited by 49
- ValuativeRel.mul_vle_mul_rightproof · cited by 5
- ValuativeRel.vle.trans_vltproof · cited by 4
- ValuativeRel.mul_vlt_mul_leftproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.