reserve X for OrtAfPl;
reserve o,a,a1,a2,a3,a4,b,b1,b2,b3,b4,c,c1,c2,c3,d,d1,d2,d3,d4,e1,e2 for
  Element of X;
reserve a29,a39,b29,x9 for Element of the AffinStruct of X;
reserve A,K,M,N for Subset of X;
reserve A9,K9 for Subset of the AffinStruct of X;

theorem Th4:
  A is being_line & a in A & b in A & c in A implies LIN a,b,c
proof
  assume that
A1: A is being_line and
A2: a in A and
A3: b in A and
A4: c in A;
  reconsider a9=a,b9=b,c9=c as Element of the AffinStruct of X;
  reconsider A9=A as Subset of the AffinStruct of X;
  A9 is being_line by A1,ANALMETR:43;
  then LIN a9,b9,c9 by A2,A3,A4,AFF_1:21;
  hence thesis by ANALMETR:40;
end;
