Theorems · Theorem · number theory
Height.logHeight_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.logHeight (x * y) ≤ Height.logHeight x + Height.logHeight yThe logarithmic height of a pointwise product of tuples is bounded by the sum of their logarithmic heights.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- Real.logproof · cited by 939
- ne_of_gtproof · cited by 637
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- Height.mulHeightproof · cited by 64
- Real.log_le_logproof · cited by 39
- Height.logHeightstatement · cited by 35
- Height.mulHeight_posproof · cited by 13
- Height.mulHeight_mul_leproof · cited by 2
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