English
From a prime ideal I, one can construct a PrimePair P via F := IsPrime I's compl_filter converted to a PFilter, with isCompl_I_F ensuring complementarity.
Русский
Изprime-идеала I можно построить PrimePair P через F := compl_filter, преобразованный к PFilter; свойство isCompl_I_F обеспечивает дополнение.
LaTeX
$$$\\text{toPrimePair} : IsPrime I \\Rightarrow \\text{PrimePair } P$ (construction with $F := h.compl_filter.toPFilter$ and $isCompl_I_F$).$$
Lean4
/-- Create an element of type `Order.Ideal.PrimePair` from an ideal satisfying the predicate
`Order.Ideal.IsPrime`. -/
def toPrimePair {I : Ideal P} (h : IsPrime I) : PrimePair P :=
{ I
F := h.compl_filter.toPFilter
isCompl_I_F := isCompl_compl }
