pythagoreanTriple_comm — Mathlib

English

If x, y, z form a Pythagorean triple, then swapping x and y yields a Pythagorean triple as well; x^2 + y^2 = z^2 iff y^2 + x^2 = z^2.

Русский

Если x, y, z образуют Пифагорову тройку, то交换 x и y также образуют тройку; x^2 + y^2 = z^2 ⇔ y^2 + x^2 = z^2.

LaTeX

$$$PythagoreanTriple(x,y,z) \iff PythagoreanTriple(y,x,z)$$$

Lean4

/-- Pythagorean triples are interchangeable, i.e `x * x + y * y = y * y + x * x = z * z`.
This comes from additive commutativity. -/
theorem pythagoreanTriple_comm {x y z : ℤ} : PythagoreanTriple x y z ↔ PythagoreanTriple y x z :=
  by
  delta PythagoreanTriple
  rw [add_comm]

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