reserve AS for AffinSpace;
reserve A,K,M,X,Y,Z,X9,Y9 for Subset of AS;
reserve zz for Element of AS;
reserve x,y for set;
reserve x,y,z,t,u,w for Element of AS;
reserve K,X,Y,Z,X9,Y9 for Subset of AS;
reserve a,b,c,d,p,q,r,p9 for POINT of IncProjSp_of(AS);
reserve A for LINE of IncProjSp_of(AS);

theorem Th35:
  A=[X,1] & X is being_line & p on A & a on A & a<>p & not p is
  Element of AS implies a is Element of AS
proof
  assume that
A1: A=[X,1] and
A2: X is being_line and
A3: p on A and
A4: a on A and
A5: a<>p and
A6: not p is Element of AS;
  assume not thesis;
  then a=LDir(X) by A1,A2,A4,Th34;
  hence contradiction by A1,A2,A3,A5,A6,Th34;
end;
