
theorem CANFS:
  for S be non empty finite set holds Union canFS S = union S
proof
   let S be non empty finite set;
   now let x be object;
    assume x in union S; then
    consider A be set such that
A2:  x in A & A in S by TARSKI:def 4;
    A in rng canFS S by A2,DIST_2:3;
    hence x in union rng canFS S by A2,TARSKI:def 4;
   end; then
   union S c= union rng canFS S;
   hence thesis by ZFMISC_1:77;
end;
