let x be set ; :: according to REWRITE2:def 1 :: thesis: ( x in dom <*f*> implies <*f*> . x is XFinSequence )
assume x in dom <*f*> ; :: thesis: <*f*> . x is XFinSequence
then x in {1} by FINSEQ_1:4, FINSEQ_1:55;
then x = 1 by TARSKI:def 1;
hence <*f*> . x is XFinSequence by FINSEQ_1:57; :: thesis: verum