reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;

theorem Th16:
  for G be IncProjSp, a,b be POINT of G, L be LINE of G st a <> b
  holds a on a*b & b on a*b & a*b = b*a & (a on L & b on L implies L = a*b)
proof
  let G be IncProjSp, a,b be POINT of G, L be LINE of G;
  assume
A1: a <> b;
  then {a,b} on a*b by Def8;
  hence a on a*b & b on a*b & a*b = b*a by A1,Def8,INCSP_1:1;
  assume a on L & b on L;
  then {a,b} on L by INCSP_1:1;
  hence thesis by A1,Def8;
end;
