Theorems · Theorem · number theory
Height.one_le_mulHeight
∀ {K : Type u_1} [inst : Field K] [inst_1 : Height.AdmissibleAbsValues K] {ι : Type u_2} [Finite ι] (x : ι → K),
1 ≤ Height.mulHeight x- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- eq_or_neproof · cited by 1,117
- le_of_eqproof · cited by 366
- AbsoluteValueproof · cited by 363
- inv_mul_cancel₀proof · cited by 267
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- map_inv₀proof · cited by 106
- inv_ne_zeroproof · cited by 99
Cited by8
Results whose statement or proof uses this declaration.
- Height.mulHeight_posproof · cited by 13
- Height.mulHeight_eval_leproof · cited by 3
- Height.mulHeight_comp_leproof · cited by 2
- Height.mulHeight_linearMap_apply_leproof · cited by 2
- Height.mulHeight_mul_leproof · cited by 2
- Projectivization.one_le_mulHeightproof · cited by 2
- Height.logHeight_nonnegproof · cited by 1
- Height.mulHeight_sym2_leproof · cited by 1