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

theorem
  a <= 0 & -1 < a & -1 <= b implies a*b < 1
proof
  assume that
A1: 0>=a and
A2: a>-1 and
A3: b>=-1;
A4: -a<--1 by A2,Lm15;
  a*b<=(-1)*a by A1,A3,Lm28;
  hence thesis by A4,XXREAL_0:2;
end;
