reserve a,b,c,d for Real;

theorem
  a <= b implies for t1,t2 being Point of Closed-Interval-TSpace(a,b)
  holds L[01](t1,t2).(#)(0,1) = t1 & L[01](t1,t2).(0,1)(#) = t2
proof
  assume
A1: a <= b;
  let t1,t2 be Point of Closed-Interval-TSpace(a,b);
  reconsider r1 = t1, r2 = t2 as Real;
  0 = (#)(0,1) by Def1;
  hence L[01](t1,t2).(#)(0,1) = (1-0)*r1 + 0*r2 by A1,Def3
    .= t1;
  1 = (0,1)(#) by Def2;
  hence L[01](t1,t2).(0,1)(#) = (1-1)*r1 + 1*r2 by A1,Def3
    .= t2;
end;
