reserve a,a1,b,b1,x,y for Real,
  F,G,H for FinSequence of REAL,
  i,j,k,n,m for Element of NAT,
  I for Subset of REAL,
  X for non empty set,
  x1,R,s for set;
reserve A for non empty closed_interval Subset of REAL;
reserve A, B for non empty closed_interval Subset of REAL;

theorem Th3:
  for a1,a2,b1,b2 being Real holds A=[.a1,b1.] & A=[.a2,b2.]
  implies a1=a2 & b1=b2
proof
  let a1,a2,b1,b2 be Real;
  assume that
A1: A=[.a1,b1.] and
A2: A=[.a2,b2.];
  a1 <= b1 by A1,XXREAL_1:29;
  hence thesis by A1,A2,XXREAL_1:66;
end;
