MetricSpaceLawArgs

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), Prop

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 => forall (P : Prop), forall (mk : forall (dist_def_law : forall (A : PointCarrier), forall (B : PointCarrier), @Eq.{u} Scalar (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B) (@sqrt.{u} Scalar sqrt_fn (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B))), forall (dist_nonneg_law : forall (A : PointCarrier), forall (B : PointCarrier), le_rel zero (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B)), forall (distance_symm_law : forall (A : PointCarrier), forall (B : PointCarrier), @Eq.{u} Scalar (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B) (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op B A)), forall (distance_zero_iff_eq_law : forall (A : PointCarrier), forall (B : PointCarrier), forall (R : Prop), forall (mk : forall (forward : forall (h : @Eq.{u} Scalar (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B) zero), @Eq.{p} PointCarrier A B), forall (backward : forall (h : @Eq.{p} PointCarrier A B), @Eq.{u} Scalar (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B) zero), R), R), forall (triangle_inequality_law : forall (A : PointCarrier), forall (B : PointCarrier), forall (C : PointCarrier), le_rel (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A C) (add (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op A B) (@dist.{p,u,v} Scalar sqrt_fn Vector inner PointCarrier disp_op B C))), P), P