reserve S for IncStruct;
reserve A,B,C,D for POINT of S;
reserve L for LINE of S;
reserve P for PLANE of S;
reserve F,G for Subset of the Points of S;

theorem Th1:
  for S being IncProjStr, L being LINE of S, A, B being POINT of S
  holds {A,B} on L iff A on L & B on L
proof
  let S be IncProjStr, L be LINE of S, A, B be POINT of S;
  thus {A,B} on L implies A on L & B on L
  proof
A1: A in {A,B} & B in {A,B} by TARSKI:def 2;
    assume {A,B} on L;
    hence thesis by A1;
  end;
  assume
A2: A on L & B on L;
  let C be POINT of S;
  assume C in {A,B};
  hence thesis by A2,TARSKI:def 2;
end;
