theorem
  Funcs(<*X*>,Y) = <*Funcs(X,Y)*>
proof
A1: dom <*X*> = Seg 1 by FINSEQ_1:def 8;
A2: dom Funcs(<*X*>,Y) = dom <*X*> by FUNCT_6:def 8;
  then reconsider p = Funcs(<*X*>,Y) as FinSequence by A1,FINSEQ_1:def 2;
  <*X*>.1 = X & 1 in Seg 1 by FINSEQ_1:2,TARSKI:def 1;
  then p.1 = Funcs(X,Y) by A1,FUNCT_6:def 8;
  hence thesis by A2,A1,FINSEQ_1:def 8;
end;
