reserve x,y for set;
reserve C,C9,D,D9,E for non empty set;
reserve c for Element of C;
reserve c9 for Element of C9;
reserve d,d1,d2,d3,d4,e for Element of D;
reserve d9 for Element of D9;
reserve i,j for natural Number;
reserve F for Function of [:D,D9:],E;
reserve p,q for FinSequence of D,
  p9,q9 for FinSequence of D9;
reserve f,f9 for Function of C,D,
  h for Function of D,E;
reserve T,T1,T2,T3 for Tuple of i,D;
reserve T9 for Tuple of i, D9;
reserve S for Tuple of j, D;
reserve S9 for Tuple of j, D9;

theorem Th17:
  F.:(i|->d,i|->d9) = i |-> (F.(d,d9))
proof
  [d,d9] in [:D,D9:] by ZFMISC_1:def 2;
  then [d,d9] in dom F by FUNCT_2:def 1;
  hence thesis by Th7;
end;
