English
The subtype of L-projections carries a maximum: the join of P and Q is given by the element with value P + Q − P Q and property join.
Русский
Подтип L-проекций имеет максимальный элемент: их объединение задается элементом с значением P+Q−PQ и свойством верхней границы.
LaTeX
$$⊔ defines a max on the subtype by $(P,Q) \\mapsto P+Q-PQ$ with the property of L-projection.$$
Lean4
noncomputable instance : NormedAddCommGroup ℍ :=
@InnerProductSpace.Core.toNormedAddCommGroup ℝ ℍ _ _ _
{ toInner := inferInstance
conj_inner_symm := fun x y => by simp [inner_def, mul_comm]
re_inner_nonneg := fun _ => normSq_nonneg
definite := fun _ => normSq_eq_zero.1
add_left := fun x y z => by simp only [inner_def, add_mul, re_add]
smul_left := fun x y r => by simp [inner_def] }
