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 Th20:
  l = [[dom l,cod l],l`2]
proof
  consider g,C1,C2 such that
A1: l = [[C1,C2],g] and
  union C2 = {} implies union C1 = {} and
  g is Function of union C1,union C2 and
  for x,y st {x,y} in C1 holds {g.x,g.y} in C2 by Th18;
  thus thesis by A1;
end;
