 reserve n for Nat;
 reserve s1 for sequence of Euclid n,
         s2 for sequence of REAL-NS n;
reserve r,s for Real;

theorem
  for a,b being Real,Iab being non empty closed_interval Subset of REAL st
  a <= b & Iab = [.a,b.] holds
  for Dab being Division of Iab st len Dab = 1 holds Dab = <*b*>
  proof
    let a,b be Real, Iab be non empty closed_interval Subset of REAL;
    assume that
A1: a <= b and
A2: Iab = [.a,b.];
    let Dab be Division of Iab;
    assume
A3: len Dab = 1;
    then consider d be Real such that
A4: Dab = <*Dab.1*> by FINSEQ_1:40;
    Dab.1 = upper_bound Iab by A3,INTEGRA1:def 2
         .= b by A1,A2,JORDAN5A:19;
    hence thesis by A4;
  end;
