let I be non empty set ; :: thesis: for A being non-Empty TopStruct-yielding ManySortedSet of
for x being Point of (Segre_Product A) holds x is ManySortedSet of
let A be non-Empty TopStruct-yielding ManySortedSet of ; :: thesis: for x being Point of (Segre_Product A) holds x is ManySortedSet of
let x be Point of (Segre_Product A); :: thesis: x is ManySortedSet of
consider f being Function such that
A1: ( x = f & dom f = dom (Carrier A) & ( for a being set st a in dom (Carrier A) holds
f . a in (Carrier A) . a ) ) by CARD_3:def 5;
dom f = I by A1, PARTFUN1:def 4;
hence x is ManySortedSet of by PARTFUN1:def 4, RELAT_1:def 18, A1; :: thesis: verum