let I, J be Interval; :: thesis: ( I is right_open_interval & J is right_open_interval & I meets J implies I /\ J is Interval )
assume A1: ( I is right_open_interval & J is right_open_interval & I meets J ) ; :: thesis: I /\ J is Interval
then consider p being Real, q being R_eal such that
A2: I = [.p,q.[ ;
consider r being Real, s being R_eal such that
A3: J = [.r,s.[ by A1;
A4: I /\ J = [.(max (r,p)),(min (s,q)).[ by A2, A3, XXREAL_1:139;
( max (p,r) is Real & min (q,s) is R_eal ) by XXREAL_0:def 1;
then I /\ J is right_open_interval by A4;
hence I /\ J is Interval ; :: thesis: verum