
theorem Th8:
  for L being RelStr, a,b,c being Element of L holds (a is_<=_than
  {b,c} iff a <= b & a <= c) & (a is_>=_than {b,c} iff b <= a & c <= a)
proof
  let L be RelStr, a,b,c be Element of L;
A1: b in {b,c} & c in {b,c} by TARSKI:def 2;
  hence a is_<=_than {b,c} implies a <= b & a <= c;
  thus a <= b & a <= c implies a is_<=_than {b,c} by TARSKI:def 2;
  thus a is_>=_than {b,c} implies a >= b & a >= c by A1;
  assume
A2: a >= b & a >= c;
  let c be Element of L;
  thus thesis by A2,TARSKI:def 2;
end;
