reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem Th58:
  congr a,b,c,d implies a,c // b,d
proof
  assume
A1: congr a,b,c,d;
  then
A2: a<>b implies thesis by Th49;
  now
    assume
A3: a=b;
    then c =d by A1,Th54;
    hence thesis by A3,Th1;
  end;
  hence thesis by A2;
end;
