theorem Th19:
  a,b,c is_a_triangle & {a,b} on P & {a,c} on Q implies P<>Q
proof
  assume that
A1: a,b,c is_a_triangle and
A2: {a,b} on P and
A3: {a,c} on Q;
A4: c on Q by A3,INCSP_1:1;
  a on P & b on P by A2,INCSP_1:1;
  hence thesis by A1,A4,Th5;
end;
