let t1 be Real; :: thesis: { |[sb,tb]| where sb, tb is Real : tb < t1 } is Subset of (REAL 2)
{ |[sd,td]| where sd, td is Real : td < t1 } c= REAL 2
proof
let y be object ; :: according to TARSKI:def 3 :: thesis: ( not y in { |[sd,td]| where sd, td is Real : td < t1 } or y in REAL 2 )
assume y in { |[sd,td]| where sd, td is Real : td < t1 } ; :: thesis: y in REAL 2
then consider s7, t7 being Real such that
A1: |[s7,t7]| = y and
t7 < t1 ;
|[s7,t7]| in the carrier of (TOP-REAL 2) ;
hence y in REAL 2 by A1, EUCLID:22; :: thesis: verum
end;
hence { |[sb,tb]| where sb, tb is Real : tb < t1 } is Subset of (REAL 2) ; :: thesis: verum