reserve x,y,z,a,b,c,X,A for set;
reserve C,D for Coherence_Space;
reserve T for Tolerance of union C;

theorem
  union C in C implies C = bool union C
proof
  assume
A1: union C in C;
  thus C c= bool union C by ZFMISC_1:82;
  let x be object;
  assume x in bool union C;
  hence thesis by A1,CLASSES1:def 1;
end;
