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;
reserve O for connected non empty Poset;
reserve R,Q for array of O;
reserve T for non empty array of O;
reserve p,q,r,s for Element of dom T;
reserve A for array, B for permutation of A;

theorem Th82:
  B in Funcs(dom A, rng A)
  proof
    dom B = dom A & rng B = rng A by Th37;
    hence thesis by FUNCT_2:def 2;
  end;
