theorem Th61:
  a,b _|_ c,d implies a,b _|_ d,c & b,a _|_ c,d & b,a _|_ d,c & c,
  d _|_ a,b & c,d _|_ b,a & d,c _|_ a,b & d,c _|_ b,a
proof
  assume
A1: a,b _|_ c,d;
  then a,b _|_ d,c by Def7;
  then
A2: d,c _|_ a,b by Def7;
  then d,c _|_ b,a by Def7;
  then b,a _|_ d,c by Def7;
  then b,a _|_ c,d by Def7;
  hence thesis by A1,A2,Def7;
end;
