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 non-ascending or not B is non-descending ) by A1;

suppose B is non-ascending ; :: thesis: B is convergent

hence B is convergent by Th64; :: thesis: verum

end;

suppose B is non-descending ; :: thesis: B is convergent

hence B is convergent by Th63; :: thesis: verum

end;

end;