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 ternary 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 FUNCT_7:def 1;
arity f = 3 by COMPUT_1:def 27;
hence dom (Den (In 3,(dom the charact of A)),A) = 3 -tuples_on the carrier of A by A1, COMPUT_1:25; :: thesis: verum