English
If HasAffineProperty holds for P and Q, then HasAffineProperty P.diagonal Q.diagonal.
Русский
Если HasAffineProperty держится для P и Q, то HasAffineProperty P.diagonal Q.diagonal.
LaTeX
$$HasAffineProperty P.diagonal Q.diagonal$$
Lean4
instance (P) {Q} [HasAffineProperty P Q] : HasAffineProperty P.diagonal Q.diagonal
where
isLocal_affineProperty :=
letI := HasAffineProperty.isLocal_affineProperty P;
inferInstance
eq_targetAffineLocally' := by
ext X Y f
letI := HasAffineProperty.isLocal_affineProperty P
constructor
· exact fun H U ↦ HasAffineProperty.diagonal_of_diagonal_of_isPullback P (isPullback_morphismRestrict f U).flip H
·
exact fun H ↦
HasAffineProperty.diagonal_of_openCover_diagonal P f Y.affineCover
(fun i ↦ of_targetAffineLocally_of_isPullback (.of_hasPullback _ _) H)