let X be set ; :: thesis: for B being SetSequence of X st B is monotone holds
B is convergent
let B be SetSequence of X; :: thesis: ( B is monotone implies B is convergent )
assume A1: B is monotone ; :: thesis: B is convergent
per cases ( not B is V55() or not B is V56() ) by A1;
suppose B is V55() ; :: thesis: B is convergent
hence B is convergent by Th64; :: thesis: verum
end;
suppose B is V56() ; :: thesis: B is convergent
hence B is convergent by Th63; :: thesis: verum
end;
end;