theorem Satz4p17:
  a <> b & Collinear a,b,c & a,p equiv a,q & b,p equiv b,q implies
  c,p equiv c,q
  proof
    assume
A1: a <> b & Collinear a,b,c & a,p equiv a,q & b,p equiv b,q;
    a,b,c,p FS a,b,c,q
    proof
      a,b equiv a,b & a,c equiv a,c & b,c equiv b,c by Satz2p1;
      hence thesis by A1,GTARSKI1:def 3;
    end;
    hence c,p equiv c,q by A1,Satz4p16;
  end;
