set D = { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } ;
let c1, c2 be Cardinal; :: thesis: ( c1, { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent & c2, { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent implies c1 = c2 )
assume ( c1, { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent & c2, { [x,y,a,b] where x, y is Element of A, a, b is Element of L : d . (x,y) <= a "\/" b } are_equipotent ) ; :: thesis: c1 = c2
then c1,c2 are_equipotent by WELLORD2:15;
hence c1 = c2 by CARD_1:2; :: thesis: verum