function ProxFA = prox_F_tightframe(ProxF,K,KS,c,y)
% prox_F_tightframe - compute the proximal operator of F o A, where A(x) = K(x)-y, K is a TF with constant c.
%
%   ProxFS = prox_F_tightframe(ProxF);
%
%   Compute the proximity callback of F o A given the
%   callbacks of the proximity operator of F, of K and its adjoint K^*.
%
%   Use the identity:
%       prox_{mu F o A}(x) = x + c^{-1}K^*((prox_{mu c F} - Id)(K x - y)
%

ic = 1/c;
ProxFA = @(x,mu)x + ic*KS(ProxF(K(x)-y,mu*c)-(K(x)-y));