Theorems · Theorem · number theory
GaussianInt.norm_le_norm_mul_left
∀ (x : GaussianInt) {y : GaussianInt}, y ≠ 0 → (Zsqrtd.norm x).natAbs ≤ (Zsqrtd.norm (x * y)).natAbs- Defined in
- Mathlib.NumberTheory.Zsqrtd.GaussianInt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- GaussianIntstatement and proof · cited by 37
- Zsqrtd.normstatement and proof · cited by 35
- le_mul_of_one_le_rightproof · cited by 15
- Zsqrtd.norm_mulproof · cited by 4
- GaussianInt.norm_posproof · cited by 1
- GaussianInt.abs_natCast_normproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- GaussianInt.mod_four_eq_three_of_nat_prime_of_primeproof · cited by 1