reconsider f = the charact of A . 2 as non empty homogeneous quasi_total 2 -ary PartFunc of ( the carrier of A *), the carrier of A by Def11;
2 in dom the charact of A by Def11;
then A1: Den ((In (2,(dom the charact of A))),A) = f by SUBSET_1:def 8;
then dom f = 2 -tuples_on the carrier of A by Th44;
then <*I1,I2*> in dom f by FINSEQ_2:137;
hence (Den ((In (2,(dom the charact of A))),A)) . <*I1,I2*> is Algorithm of A by A1, PARTFUN1:4; :: thesis: verum