set D = { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } ;

take card { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } ; :: thesis: card { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } , { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent

thus card { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } , { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent by CARD_1:def 2; :: thesis: verum

take card { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } ; :: thesis: card { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } , { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent

thus card { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } , { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent by CARD_1:def 2; :: thesis: verum