let A be non-empty with_if-instruction UAStr ; :: thesis: dom (Den ((In (3,(dom the charact of A))),A)) = 3 -tuples_on the carrier of A
reconsider f = the charact of A . 3 as non empty homogeneous quasi_total 3 -ary PartFunc of ( the carrier of A *), the carrier of A by Def12;
3 in dom the charact of A by Def12;
then A1: Den ((In (3,(dom the charact of A))),A) = f by SUBSET_1:def 8;
arity f = 3 by COMPUT_1:def 21;
hence dom (Den ((In (3,(dom the charact of A))),A)) = 3 -tuples_on the carrier of A by A1, COMPUT_1:22; :: thesis: verum