English
The fixed point property of pointReflection interacts with two-nsmul injections to yield the equivalence in the previous lemma.
Русский
Свойство фиксированной точки pointReflection взаимодействует с инъективностью двухнсмулов, приводя к эквивалентности, упомянутой ранее.
LaTeX
$$$$ \text{pointReflection fixed_iff_of_injective_two_nsmul} $$$$
Lean4
/-- Adding a group element to a point, then subtracting another point,
produces the same result as subtracting the points then adding the
group element. -/
theorem vadd_vsub_assoc (g : G) (p₁ p₂ : P) : (g +ᵥ p₁) -ᵥ p₂ = g + (p₁ -ᵥ p₂) :=
by
apply vadd_right_cancel p₂
rw [vsub_vadd, add_vadd, vsub_vadd]
