reserve x,y,z,r,s for ExtReal;
reserve A,B for ext-real-membered set;

theorem Th5:
  B c= A implies for x being LowerBound of A holds x is LowerBound of B
proof
  assume
A1: B c= A;
  let x be LowerBound of A;
  let y;
  assume y in B;
  hence thesis by A1,Def2;
end;
