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

theorem Th66:
  0 <= a & a <= b & 0 <= c & c <= d implies a*c <= b*d
proof
  assume that
A1: 0 <= a and
A2: a <= b and
A3: 0 <= c and
A4: c <= d;
A5: a*c <= b*c by A2,A3,Lm12;
  b*c <= b*d by A1,A2,A4,Lm12;
  hence thesis by A5,XXREAL_0:2;
end;
