Theorems · Theorem · number theory
GaussianInt.normSq_le_normSq_of_re_le_of_im_le
∀ {x y : ℂ}, |x.re| ≤ |y.re| → |x.im| ≤ |y.im| → Complex.normSq x ≤ Complex.normSq y- Defined in
- Mathlib.NumberTheory.Zsqrtd.GaussianInt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 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.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Nat.cast_zeroproof · cited by 1,870
- absstatement and proof · cited by 1,814
- Complex.restatement and proof · cited by 882
- MonoidWithZeroHomstatement · cited by 704
- Complex.imstatement and proof · cited by 591
- le_of_not_gtproof · cited by 430
- Complex.normSqstatement · cited by 103
- sq_le_sqproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- GaussianInt.normSq_div_sub_div_lt_oneproof · cited by 1