let n be Ordinal; :: thesis: for T being TermOrder of n
for b1, b2 being bag of n st b1 <= b2,T & b2 <= b1,T holds
b1 = b2
let T be TermOrder of n; :: thesis: for b1, b2 being bag of n st b1 <= b2,T & b2 <= b1,T holds
b1 = b2
let b1, b2 be bag of n; :: thesis: ( b1 <= b2,T & b2 <= b1,T implies b1 = b2 )
field T = Bags n by ORDERS_1:12;
then A1: T is_antisymmetric_in Bags n by RELAT_2:def 12;
assume ( b1 <= b2,T & b2 <= b1,T ) ; :: thesis: b1 = b2
then A2: ( [b1,b2] in T & [b2,b1] in T ) ;
( b1 is Element of Bags n & b2 is Element of Bags n ) by PRE_POLY:def 12;
hence b1 = b2 by A2, A1, RELAT_2:def 4; :: thesis: verum