Theorems · Theorem · commutative algebra
ValuativeRel.mul_vlt_mul_of_vle_of_vlt
∀ {R : Type u_2} [inst : Ring R] [inst_1 : ValuativeRel R] {a b c d : R}, a ≤ᵥ b → c <ᵥ d → 0 <ᵥ a → a * c <ᵥ b * d- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- RingValuativeRel
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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_leftproof · cited by 6
- ValuativeRel.vlt.trans_vleproof · cited by 4
- ValuativeRel.mul_vlt_mul_rightproof · cited by 2
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