let u be ExtReal; :: thesis: for x being Real holds
( x in [.u,+infty.[ iff u <= x )
let x be Real; :: thesis: ( x in [.u,+infty.[ iff u <= x )
x in REAL by XREAL_0:def 1;
then x < +infty by XXREAL_0:9;
hence ( x in [.u,+infty.[ iff u <= x ) by Th3; :: thesis: verum