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);

theorem Th29:
  a c= X implies Total a in Toler_on_subsets(X)
proof
  set F = the set of all Toler(Y) where Y is Subset of X;
  assume a c= X;
  then
A1: Toler(a) in F;
  Total a in Toler(a) by Def15;
  hence thesis by A1,TARSKI:def 4;
end;
