reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  0 <= d & a <= b implies a <= (1-d)*a+d*b
proof
  assume that
A1: 0<=d and
A2: a<=b;
  d*a<=d*b by A1,A2,Lm12;
  then (1-d)*a+d*a<=(1-d)*a+d*b by Lm6;
  hence thesis;
end;
