reserve x,y,y1,y2 for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,h,g,h1 for Membership_Func of C;

theorem
  f \+\ EMF(C) = f
proof
  thus f \+\ EMF(C) = max(min(f,UMF(C)),min(1_minus(f),EMF(C))) by Th39
    .= max(f,min(1_minus(f),EMF(C))) by Th17
    .= max(f,EMF(C)) by Th17
    .= f by Th17;
end;
