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

theorem
  0 <= a & a < 1 & b <= 1 implies a*b < 1
proof
  assume that
A1: 0<=a and
A2: a<1 and
A3: b<=1;
  a*b<=1*a by A1,A3,Lm12;
  hence thesis by A2,XXREAL_0:2;
end;
