pythagorean_distance_general

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 (metric_pythagorean_target : forall (A : PointCarrier), forall (B : PointCarrier), forall (C : PointCarrier), forall (h : @RightTriangle.{p,u,v} Scalar zero Vector inner PointCarrier disp_op A B C), @Eq.{u} Scalar (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op B C)) (add (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B)) (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A C)))), forall (A : PointCarrier), forall (B : PointCarrier), forall (C : PointCarrier), forall (h : @RightTriangle.{p,u,v} Scalar zero Vector inner PointCarrier disp_op A B C), @Eq.{u} Scalar (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op B C)) (add (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B)) (@sq.{u} Scalar mul (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A C)))

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 metric_pythagorean_target => fun A => fun B => fun C => fun h => metric_pythagorean_target A B C h