Theorems · Theorem · number theory
PythagoreanTriple.normalize
∀ {x y z : ℤ}, PythagoreanTriple x y z → PythagoreanTriple (x / ↑(x.gcd y)) (y / ↑(x.gcd y)) (z / ↑(x.gcd y))- Defined in
- Mathlib.NumberTheory.PythagoreanTriples
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- CharP.cast_eq_zeroproof · cited by 357
- pos_iff_ne_zeroproof · cited by 180
- PythagoreanTriplestatement and proof · cited by 24
- EuclideanDomain.div_zeroproof · cited by 17
- PythagoreanTriple.gcd_dvdproof · cited by 2
- Int.exists_gcd_one'proof · cited by 2
- PythagoreanTriple.mul_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- PythagoreanTriple.classifiedproof · cited by 1
- PythagoreanTriple.isClassified_of_normalize_isPrimitiveClassifiedstatement and proof · cited by 1