let a, b be real number ; :: thesis: ( a <= b implies the carrier of (Closed-Interval-MSpace a,b) = [.a,b.] )
assume A1: a <= b ; :: thesis: the carrier of (Closed-Interval-MSpace a,b) = [.a,b.]
then reconsider P = [.a,b.] as non empty Subset of RealSpace by METRIC_1:def 14, XXREAL_1:1;
thus the carrier of (Closed-Interval-MSpace a,b) = the carrier of (RealSpace | P) by A1, Def3
.= [.a,b.] by Def2 ; :: thesis: verum