let X be set ; :: thesis: for b1, b2 being bag of X holds
( b1 divides lcm (b1,b2) & b2 divides lcm (b1,b2) )
let b1, b2 be bag of X; :: thesis: ( b1 divides lcm (b1,b2) & b2 divides lcm (b1,b2) )
set bb = lcm (b1,b2);

now :: thesis: for k being object holds b1 . k <= (lcm (b1,b2)) . k

let k be object ; :: thesis: b1 . k <= (lcm (b1,b2)) . k
b1 . k <= max ((b1 . k),(b2 . k)) by XXREAL_0:25;
hence b1 . k <= (lcm (b1,b2)) . k by Def2; :: thesis: verum

end;

hence b1 divides lcm (b1,b2) by PRE_POLY:def 11; :: thesis: b2 divides lcm (b1,b2)

now :: thesis: for k being object holds b2 . k <= (lcm (b1,b2)) . k

let k be object ; :: thesis: b2 . k <= (lcm (b1,b2)) . k
b2 . k <= max ((b1 . k),(b2 . k)) by XXREAL_0:25;
hence b2 . k <= (lcm (b1,b2)) . k by Def2; :: thesis: verum

end;

hence b2 divides lcm (b1,b2) by PRE_POLY:def 11; :: thesis: verum