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

theorem
  a < -1 & b <= -1 implies 1 < a*b
proof
  assume that
A1: a<-1 and
A2: b<=-1;
A3: -b>=--1 by A2,Lm14;
  a*b>b*(-1) by A1,A2,Lm24;
  hence thesis by A3,XXREAL_0:2;
end;
