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 Th22:
  dom l2 = cod l1 implies (l2*l1)`2 = l2`2*l1`2 & dom(l2*l1) = dom
  l1 & cod(l2*l1) = cod l2
proof
  assume dom l2 = cod l1;
  then [[dom l1,cod l2],l2`2*l1`2] = l2*l1 by Def10
    .= [[dom(l2*l1),cod(l2*l1)],(l2*l1)`2] by Th20;
  hence thesis by Lm2,XTUPLE_0:1;
end;
