partial_x_derivative_from_args

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 (x : X), forall (y : X), X), forall (xneg : forall (x : 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 (x : Y), forall (y : Y), Y), forall (yneg : forall (y : Y), Y), forall (ysmul : forall (a : Scalar), forall (y : Y), Y), forall (ynorm : forall (y : Y), Scalar), forall (Z : Sort z), forall (zzero : Z), forall (zadd : forall (x : Z), forall (y : Z), Z), forall (zneg : forall (z : Z), Z), forall (zsmul : forall (a : Scalar), forall (z : Z), Z), forall (znorm : forall (z : Z), Scalar), forall (Product : Sort p), forall (pzero : Product), forall (padd : forall (x : Product), forall (y : Product), Product), forall (pneg : forall (x : Product), Product), forall (psmul : forall (a : Scalar), forall (x : Product), Product), forall (pnorm : forall (x : Product), Scalar), forall (pair : forall (x : X), forall (y : Y), Product), forall (fst : forall (point : Product), X), forall (snd : forall (point : Product), Y), forall (F : forall (point : Product), Z), forall (args : @PartialDerivativeRuleArgs.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F), forall (base_x : X), forall (base_y : Y), forall (dF : forall (h : Product), Z), forall (F_bound : Scalar), forall (F_remainder : forall (r : Z), Prop), forall (partial_x_bound : Scalar), forall (partial_x_remainder : forall (r : Z), Prop), forall (partial_y_bound : Scalar), forall (partial_y_remainder : forall (r : Z), Prop), forall (F_at : @FrechetDerivativeAt.{u,p,z} Scalar zero one add neg sub mul le_rel Product pzero padd pneg psmul pnorm Z zzero zadd zneg zsmul znorm F (pair base_x base_y) dF F_bound F_remainder), @FrechetDerivativeAt.{u,v,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Z zzero zadd zneg zsmul znorm (@PartialXMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F base_y) base_x (@PartialXDerivativeMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F dF) partial_x_bound partial_x_remainder

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 Z => fun zzero => fun zadd => fun zneg => fun zsmul => fun znorm => fun Product => fun pzero => fun padd => fun pneg => fun psmul => fun pnorm => fun pair => fun fst => fun snd => fun F => fun args => fun base_x => fun base_y => fun dF => fun F_bound => fun F_remainder => fun partial_x_bound => fun partial_x_remainder => fun partial_y_bound => fun partial_y_remainder => fun F_at => args base_x base_y dF F_bound F_remainder partial_x_bound partial_x_remainder partial_y_bound partial_y_remainder F_at (@FrechetDerivativeAt.{u,v,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Z zzero zadd zneg zsmul znorm (@PartialXMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F base_y) base_x (@PartialXDerivativeMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F dF) partial_x_bound partial_x_remainder) (fun (partial_x_at : @FrechetDerivativeAt.{u,v,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Z zzero zadd zneg zsmul znorm (@PartialXMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F base_y) base_x (@PartialXDerivativeMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F dF) partial_x_bound partial_x_remainder) => fun (partial_y_at : @FrechetDerivativeAt.{u,w,z} Scalar zero one add neg sub mul le_rel Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm (@PartialYMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F base_x) base_y (@PartialYDerivativeMap.{p,u,v,w,z} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm Z zzero zadd zneg zsmul znorm Product pzero padd pneg psmul pnorm pair fst snd F dF) partial_y_bound partial_y_remainder) => partial_x_at)