Theorems · Theorem · number theory
Height.mulHeight_eq_one_of_subsingleton
∀ {K : Type u_1} [inst : Field K] [inst_1 : Height.AdmissibleAbsValues K] {ι : Type u_5} [Subsingleton ι] (x : ι → K),
Height.mulHeight x = 1- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 7 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.
Cites11
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
- eq_or_neproof · cited by 1,117
- inv_mul_cancel₀proof · cited by 267
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- inv_ne_zeroproof · cited by 99
- Height.mulHeightstatement and proof · cited by 64
- Function.ne_iffproof · cited by 40
- Height.mulHeight_zeroproof · cited by 17
- Height.mulHeight_smul_eq_mulHeightproof · cited by 6
- Height.mulHeight_oneproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Height.mulHeight₁_div_eq_mulHeightproof · cited by 2
- Height.mulHeight_linearMap_apply_leproof · cited by 2
- Height.mulHeight_mul_leproof · cited by 2
- Height.mulHeight_eval_geproof · cited by 2
- Height.logHeight_eq_zero_of_subsingletonproof · cited by 1
- Height.mulHeight_eval_ge'proof · cited by 1
- Height.logHeight_eval_geproof · cited by 1