implicit_phi_partial_y_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 (XY : Sort p), forall (xyzero : XY), forall (xyadd : forall (x : XY), forall (y : XY), XY), forall (xyneg : forall (x : XY), XY), forall (xysmul : forall (a : Scalar), forall (x : XY), XY), forall (xynorm : forall (x : XY), Scalar), forall (pairXY : forall (x : X), forall (y : Y), XY), forall (fstXY : forall (point : XY), X), forall (sndXY : forall (point : XY), Y), forall (XZ : Sort q), forall (xzzero : XZ), forall (xzadd : forall (x : XZ), forall (y : XZ), XZ), forall (xzneg : forall (x : XZ), XZ), forall (xzsmul : forall (a : Scalar), forall (x : XZ), XZ), forall (xznorm : forall (x : XZ), Scalar), forall (pairXZ : forall (x : X), forall (z : Z), XZ), forall (fstXZ : forall (point : XZ), X), forall (sndXZ : forall (point : XZ), Z), forall (F : forall (point : XY), Z), forall (base_x : X), forall (base_y : Y), forall (dF : forall (h : XY), Z), forall (dFx : forall (h : X), Z), forall (dFy : forall (h : Y), Z), forall (dFy_inv : forall (z : Z), Y), 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 (phi_bound : Scalar), forall (phi_remainder : forall (r : XZ), Prop), forall (args : @ImplicitPhiDerivativeArgs.{p,q,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 XY xyzero xyadd xyneg xysmul xynorm pairXY fstXY sndXY XZ xzzero xzadd xzneg xzsmul xznorm pairXZ fstXZ sndXZ F base_x base_y dF dFx dFy dFy_inv F_bound F_remainder partial_x_bound partial_x_remainder partial_y_bound partial_y_remainder phi_bound phi_remainder), @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 XY xyzero xyadd xyneg xysmul xynorm pairXY fstXY sndXY F base_x) base_y dFy partial_y_bound partial_y_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 XY => fun xyzero => fun xyadd => fun xyneg => fun xysmul => fun xynorm => fun pairXY => fun fstXY => fun sndXY => fun XZ => fun xzzero => fun xzadd => fun xzneg => fun xzsmul => fun xznorm => fun pairXZ => fun fstXZ => fun sndXZ => fun F => fun base_x => fun base_y => fun dF => fun dFx => fun dFy => fun dFy_inv => fun F_bound => fun F_remainder => fun partial_x_bound => fun partial_x_remainder => fun partial_y_bound => fun partial_y_remainder => fun phi_bound => fun phi_remainder => fun args => args (@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 XY xyzero xyadd xyneg xysmul xynorm pairXY fstXY sndXY F base_x) base_y dFy partial_y_bound partial_y_remainder) (fun (F_at_arg : @FrechetDerivativeAt.{u,p,z} Scalar zero one add neg sub mul le_rel XY xyzero xyadd xyneg xysmul xynorm Z zzero zadd zneg zsmul znorm F (pairXY base_x base_y) dF F_bound F_remainder) => fun (partial_x_arg : @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 XY xyzero xyadd xyneg xysmul xynorm pairXY fstXY sndXY F base_y) base_x dFx partial_x_bound partial_x_remainder) => fun (partial_y_arg : @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 XY xyzero xyadd xyneg xysmul xynorm pairXY fstXY sndXY F base_x) base_y dFy partial_y_bound partial_y_remainder) => fun (phi_at_arg : @FrechetDerivativeAt.{u,p,q} Scalar zero one add neg sub mul le_rel XY xyzero xyadd xyneg xysmul xynorm XZ xzzero xzadd xzneg xzsmul xznorm (@ImplicitPhi.{p,q,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 XY xyzero xyadd xyneg xysmul xynorm pairXY fstXY sndXY XZ xzzero xzadd xzneg xzsmul xznorm pairXZ fstXZ sndXZ F base_x base_y) (pairXY base_x base_y) (@ImplicitPhiDerivativeMap.{p,q,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 XY xyzero xyadd xyneg xysmul xynorm pairXY fstXY sndXY XZ xzzero xzadd xzneg xzsmul xznorm pairXZ fstXZ sndXZ F base_x base_y dFx dFy dFy_inv) phi_bound phi_remainder) => partial_y_arg)