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 set ; :: 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 ex s7, t7 being Real st
( |[s7,t7]| = y & t7 < t1 ) ;
hence y in REAL 2 ; :: thesis: verum

end;

hence { |[sb,tb]| where sb, tb is Real : tb < t1 } is Subset of (REAL 2) ; :: thesis: verum