 reserve R for 1-sorted;
 reserve X,Y for Subset of R;
 reserve R for finite 1-sorted;
 reserve X,Y for Subset of R;
 reserve R for finite Approximation_Space;
 reserve X,Y,Z,W for Subset of R;

theorem  ::: Theorem 4.1 d) from Gomolinska's "A Comparative Study..."
  for R being finite Approximation_Space,
      u being Element of R,
      x,y being Subset of R st
   u in (Flip f_1 R).x & (UncertaintyMap R).u = y
    holds kappa (y, x) = 1
  proof
    let R be finite Approximation_Space,
        u be Element of R,
        x,y be Subset of R;
    assume
A0: u in (Flip f_1 R).x & (UncertaintyMap R).u = y;
    (Flip f_1 R).x = { w where w is Element of R :
       (UncertaintyMap R).w c= x } by ROUGHS_5:30; then
    consider v being Element of R such that
A3: u = v & (UncertaintyMap R).v c= x by A0;
    thus thesis by Prop1a,A0,A3;
  end;
