dist_sq_eq_square_dist_from_law_packages

forall (Scalar : Sort u), forall (zero : Scalar), forall (one : Scalar), forall (add : forall (a : Scalar), forall (b : Scalar), Scalar), forall (neg : forall (a : Scalar), Scalar), forall (sub : forall (a : Scalar), forall (b : Scalar), Scalar), forall (mul : forall (a : Scalar), forall (b : Scalar), Scalar), forall (le_rel : forall (a : Scalar), forall (b : Scalar), Prop), forall (lt_rel : forall (a : Scalar), forall (b : Scalar), Prop), forall (sqrt_fn : forall (a : Scalar), Scalar), forall (Vector : Sort v), forall (vzero : Vector), forall (vadd : forall (x : Vector), forall (y : Vector), Vector), forall (vneg : forall (x : Vector), Vector), forall (smul : forall (a : Scalar), forall (x : Vector), Vector), forall (inner : forall (x : Vector), forall (y : Vector), Scalar), forall (PointCarrier : Sort p), forall (disp_op : forall (A : PointCarrier), forall (B : PointCarrier), Vector), forall (ordered_args : @OrderedFieldLawArgs.{u} Scalar zero one add neg sub mul le_rel lt_rel sqrt_fn), forall (inner_args : @InnerProductLawArgs.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul inner), forall (A : PointCarrier), forall (B : PointCarrier), @Eq.{u} Scalar (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B) (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B))

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun lt_rel => fun sqrt_fn => fun Vector => fun vzero => fun vadd => fun vneg => fun smul => fun inner => fun PointCarrier => fun disp_op => fun ordered_args => fun inner_args => fun A => fun B => @Eq.rec.{u,0} Scalar (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B)) (fun (q : Scalar) => fun (hq : @Eq.{u} Scalar (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B)) q) => @Eq.{u} Scalar q (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B))) (@Eq.refl.{u} Scalar (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B))) (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B) (@square_dist_eq_dist_sq_from_law_packages.{p,u,v} Scalar zero one add neg sub mul le_rel lt_rel sqrt_fn Vector vzero vadd vneg smul inner PointCarrier disp_op ordered_args inner_args A B)