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

theorem Th95:
  for A being non empty Subset of ExtREAL, r being Element of ExtREAL
    st inf A < r
   ex s being Element of ExtREAL st s in A & s < r
proof
  let A be non empty Subset of ExtREAL, r be Element of ExtREAL;
  assume
A1: inf A < r;
  assume
A2: for s being Element of ExtREAL st s in A holds not s < r;
  r is LowerBound of A
  proof
    let x be ExtReal;
    thus thesis by A2;
  end;
  hence contradiction by A1,Def4;
end;
