reserve r,p,x for Real;
reserve n for Element of NAT;
reserve A for non empty closed_interval Subset of REAL;
reserve Z for open Subset of REAL;

theorem
  for f,g being PartFunc of REAL,REAL,
  A being non empty closed_interval Subset of
  REAL holds |||(f,g,A)||| = |||(g,f,A)|||;
