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 Th2:
  for S being IncProjStr, L being LINE of S, A, B, C being POINT
  of S holds {A,B,C} on L iff A on L & B on L & C on L
proof
  let S be IncProjStr, L be LINE of S, A, B, C be POINT of S;
  thus {A,B,C} on L implies A on L & B on L & C on L
  proof
A1: C in {A,B,C} by ENUMSET1:def 1;
A2: A in {A,B,C} & B in {A,B,C} by ENUMSET1:def 1;
    assume {A,B,C} on L;
    hence thesis by A2,A1;
  end;
  assume
A3: A on L & B on L & C on L;
  let D be POINT of S;
  assume D in {A,B,C};
  hence thesis by A3,ENUMSET1:def 1;
end;
