reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;

theorem Th31:
  x in dom f & y in dom f implies Swap(f,x,y).y = f.x
  proof assume
A1: x in dom f & y in dom f; then
A2: Swap(f,x,y) = f+*(x,f.y)+*(y,f.x) by FUNCT_7:def 12;
    dom f = dom(f+*(x,f.y)) by FUNCT_7:30;
    hence thesis by A1,A2,FUNCT_7:31;
  end;
