let A be non-empty with_catenation UAStr ; :: thesis: dom (Den (In 2,(dom the charact of A)),A) = 2 -tuples_on the carrier of A
reconsider f = the charact of A . 2 as non empty homogeneous quasi_total binary 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 FUNCT_7:def 1;
arity f = 2 by COMPUT_1:def 26;
hence dom (Den (In 2,(dom the charact of A)),A) = 2 -tuples_on the carrier of A by A1, COMPUT_1:25; :: thesis: verum