Theorems · Theorem · number theory
Height.mulHeight_pos
∀ {K : Type u_1} [inst : Field K] [inst_1 : Height.AdmissibleAbsValues K] {ι : Type u_2} [Finite ι] (x : ι → K),
0 < Height.mulHeight x- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- LT.lt.trans_leproof · cited by 678
- zero_lt_oneproof · cited by 598
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- Height.mulHeightstatement · cited by 64
- Height.one_le_mulHeightproof · cited by 8
Cited by13
Results whose statement or proof uses this declaration.
- Height.mulHeight_eval_leproof · cited by 3
- Height.mulHeight_eval_geproof · cited by 2
- Height.mulHeight_linearMap_apply_leproof · cited by 2
- Height.logHeight_eval_leproof · cited by 1
- Height.mulHeight_sym2_leproof · cited by 1
- Height.logHeight_sym2_geproof · cited by 1
- Height.logHeight_sym2_leproof · cited by 1
- Height.mulHeight_ne_zeroproof · cited by 1
- Height.logHeight_eval_geproof · cited by 1
- Height.logHeight_fun_mul_eqproof · cited by 0
- Height.logHeight_linearMap_apply_leproof · cited by 0
- Height.logHeight_mul_leproof · cited by 0