implicit_extraction_local_inverse_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 (x_domain : forall (x : X), Prop), forall (y_domain : forall (y : Y), Prop), forall (xy_domain : forall (point : XY), Prop), forall (xz_domain : forall (target : XZ), Prop), forall (phi_inv : forall (target : XZ), XY), forall (dPhi : forall (h : XY), XZ), forall (dPhi_inv : forall (target : XZ), XY), forall (op_norm : Scalar), forall (inv_op_norm : Scalar), forall (inverse_bound : Scalar), forall (inverse_remainder : forall (r : XY), Prop), forall (args : @ImplicitFunctionExtractionArgs.{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 x_domain y_domain xy_domain xz_domain phi_inv dPhi dPhi_inv op_norm inv_op_norm inverse_bound inverse_remainder), @ImplicitPhiLocalInverseLaws.{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 x_domain y_domain xy_domain xz_domain phi_inv dPhi dPhi_inv op_norm inv_op_norm inverse_bound inverse_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 x_domain => fun y_domain => fun xy_domain => fun xz_domain => fun phi_inv => fun dPhi => fun dPhi_inv => fun op_norm => fun inv_op_norm => fun inverse_bound => fun inverse_remainder => fun args => args (@ImplicitPhiLocalInverseLaws.{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 x_domain y_domain xy_domain xz_domain phi_inv dPhi dPhi_inv op_norm inv_op_norm inverse_bound inverse_remainder) (fun (local_inverse_arg : @ImplicitPhiLocalInverseLaws.{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 x_domain y_domain xy_domain xz_domain phi_inv dPhi dPhi_inv op_norm inv_op_norm inverse_bound inverse_remainder) => fun (target_mem_arg : forall (x : X), forall (hx : x_domain x), xz_domain (@ImplicitTargetPoint.{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 x)) => fun (value_mem_projection_arg : forall (point : XY), forall (point_mem : xy_domain point), y_domain (sndXY point)) => fun (zero_projection_arg : forall (x : X), forall (hx : x_domain x), forall (target_mem : xz_domain (@ImplicitTargetPoint.{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 x)), forall (left_inverse_eq : @Eq.{q} XZ (@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 (phi_inv (@ImplicitTargetPoint.{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 x))) (@ImplicitTargetPoint.{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 x)), @Eq.{z} Z (F (@ImplicitGraphPoint.{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 x_domain y_domain xy_domain xz_domain phi_inv dPhi dPhi_inv op_norm inv_op_norm inverse_bound inverse_remainder x)) zzero) => fun (zero_to_phi_image_arg : forall (x : X), forall (y : Y), forall (zero_eq : @Eq.{z} Z (F (pairXY x y)) zzero), @Eq.{q} XZ (@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 x y)) (@ImplicitTargetPoint.{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 x)) => fun (snd_pair_arg : forall (x : X), forall (y : Y), @Eq.{w} Y (sndXY (pairXY x y)) y) => local_inverse_arg)