reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

theorem
  proj1 {[x,y],[z,t]} = {x,z} & proj2 {[x,y],[z,t]} = {y,t}
proof
A1: proj2 {[x,y]} = {y} & proj2 {[z,t]} = {t} by Th6;
  {[x,y],[z,t]} = {[x,y]} \/ {[z,t]} by ENUMSET1:1;
  then
A2: proj1 {[x,y],[z,t]} = proj1 {[x,y]} \/ proj1 {[z,t]} & proj2 {[x,y],[z,t
  ]} = proj2 {[x,y]} \/ proj2 {[z,t]} by XTUPLE_0:23,27;
  proj1 {[x,y]} = {x} & proj1 {[z,t]} = {z} by Th6;
  hence thesis by A2,A1,ENUMSET1:1;
end;
