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

theorem Th28:
  x < y implies inf ].x,y.[ = x
proof
  assume
A1: x < y;
A2: for z being LowerBound of ].x,y.[ holds z <= x
  proof
    let z be LowerBound of ].x,y.[;
    for r st x < r & r < y holds z <= r
    by XXREAL_1:4,Def2;
    hence thesis by A1,XREAL_1:228;
  end;
  x is LowerBound of ].x,y.[ by Th20;
  hence thesis by A2,Def4;
end;
