let I be non empty set ; :: thesis: for F being multMagma-Family of I
for x being set st x in the carrier of (product F) holds
x is I -defined total Function
let F be multMagma-Family of I; :: thesis: for x being set st x in the carrier of (product F) holds
x is I -defined total Function
let x be set ; :: thesis: ( x in the carrier of (product F) implies x is I -defined total Function )
assume A1: x in the carrier of (product F) ; :: thesis: x is I -defined total Function
the carrier of (product F) = product (Carrier F) by GROUP_7:def 2;
hence x is I -defined total Function by A1; :: thesis: verum