product_dist_def

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 (X : Sort v), forall (xzero : X), forall (xadd : forall (a : X), forall (b : X), X), forall (xneg : forall (a : X), X), forall (xsmul : forall (a : Scalar), forall (x : X), X), forall (xnorm : forall (x : X), Scalar), forall (Y : Sort w), forall (yzero : Y), forall (yadd : forall (a : Y), forall (b : Y), Y), forall (yneg : forall (a : Y), Y), forall (ysmul : forall (a : Scalar), forall (y : Y), Y), forall (ynorm : forall (y : Y), Scalar), forall (Product : Sort p), forall (pair : forall (x : X), forall (y : Y), Product), forall (fst : forall (point : Product), X), forall (snd : forall (point : Product), Y), forall (left : Product), forall (right : Product), @Eq.{u} Scalar (@ProductDist.{p,u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Product pair fst snd left right) (@ProductNorm.{p,u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Product pair fst snd (@ProductSub.{p,u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Product pair fst snd right left))

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun X => fun xzero => fun xadd => fun xneg => fun xsmul => fun xnorm => fun Y => fun yzero => fun yadd => fun yneg => fun ysmul => fun ynorm => fun Product => fun pair => fun fst => fun snd => fun left => fun right => @Eq.refl.{u} Scalar (@ProductDist.{p,u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Product pair fst snd left right)