theorem Th52:
  K _|_ M & K // N implies N _|_ M
proof
  assume that
A1: K _|_ M and
A2: K // N;
  consider r,s such that
A3: r<>s & M = Line(r,s) and
A4: r,s _|_ K by A1,Def13;
  r,s _|_ N by A2,A4,Th50;
  hence thesis by A3,Def13;
end;
