Theorems · Theorem · number theory
GaussianInt.normSq_div_sub_div_lt_one
∀ (x y : GaussianInt), Complex.normSq (GaussianInt.toComplex x / GaussianInt.toComplex y - GaussianInt.toComplex (x / y)) < 1
- Defined in
- Mathlib.NumberTheory.Zsqrtd.GaussianInt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- absproof · cited by 1,814
- Complex.ofRealproof · cited by 1,654
- sub_selfproof · cited by 996
Cited by1
Results whose statement or proof uses this declaration.
- GaussianInt.norm_mod_ltproof · cited by 1