let c1, c2 be Element of A; :: thesis: ( c1 <= a & c1 <= b & ( for c being Element of A st c <= a & c <= b holds
c <= c1 ) & c2 <= a & c2 <= b & ( for c being Element of A st c <= a & c <= b holds
c <= c2 ) implies c1 = c2 )
assume that
A3: ( c1 <= a & c1 <= b & ( for c being Element of A st c <= a & c <= b holds
c <= c1 ) ) and
A4: ( c2 <= a & c2 <= b & ( for c being Element of A st c <= a & c <= b holds
c <= c2 ) ) ; :: thesis: c1 = c2
( c1 <= c2 & c2 <= c1 ) by A3, A4;
hence c1 = c2 by A1, ORDERS_2:25; :: thesis: verum