Theorems · Theorem · number theory
Height.mulHeight_mul_le
∀ {K : Type u_1} [inst : Field K] [inst_1 : Height.AdmissibleAbsValues K] {ι : Type u_2} [Finite ι] (x y : ι → K),
Height.mulHeight (x * y) ≤ Height.mulHeight x * Height.mulHeight yThe multiplicative height of a pointwise product of tuples is bounded by the product of their multiplicative heights.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- mul_oneproof · cited by 3,885
- Finitestatement and proof · cited by 3,029
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- IsEmptyproof · cited by 759
- isEmpty_or_nonemptyproof · cited by 269
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- Height.mulHeightstatement and proof · cited by 64
Cited by2
Results whose statement or proof uses this declaration.
- Height.mulHeight₁_mul_leproof · cited by 2
- Height.logHeight_mul_leproof · cited by 0