let s1 be Real; :: thesis: { |[sb,tb]| where sb, tb is Real : sb <= s1 } is Subset of (TOP-REAL 2)
{ |[sb,tb]| where sb, tb is Real : sb <= s1 } c= REAL 2

proof

let y be object ; :: according to TARSKI:def 3 :: thesis: ( not y in { |[sb,tb]| where sb, tb is Real : sb <= s1 } or y in REAL 2 )
assume y in { |[sb,tb]| where sb, tb is Real : sb <= s1 } ; :: thesis: y in REAL 2
then ex s7, t7 being Real st
( |[s7,t7]| = y & s7 <= s1 ) ;
hence y in REAL 2 by Lm2; :: thesis: verum

end;

hence { |[sb,tb]| where sb, tb is Real : sb <= s1 } is Subset of (TOP-REAL 2) by EUCLID:22; :: thesis: verum