theorem Th17:
  A in nextcard A
proof
  assume not A in nextcard A;
  then
A1: card nextcard A c= card A by Th10,ORDINAL1:16;
A2: nextcard card A = nextcard A by Def2,Th16;
A3: card card A in nextcard card A by Def3;
  thus contradiction by A1,A2,A3,ORDINAL1:5;
end;
