let X, Y be set ; Funcs (<*X*>,Y) = <*(Funcs (X,Y))*>
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
Funcs (<*X*>,Y) = <*(Funcs (X,Y))*>
by A2, A1, FINSEQ_1:def 8; verum