reserve x,y,z,a,b,c,X,A for set;
reserve C,D for Coherence_Space;
reserve T for Tolerance of union C;
reserve E for Tolerance of X;
reserve C,C1,C2 for Element of CSp(X);
reserve g for Element of FuncsC(X);
reserve l,l1,l2,l3 for Element of MapsC(X);
reserve T,T1,T2 for Element of TOL(X);

theorem Th34:
  a c= X implies [id a,a] in TOL(X)
proof
  assume
A1: a c= X;
  then id a in Toler_on_subsets(X) by Th30;
  hence thesis by A1;
end;
