let n be Nat; :: thesis: for A being Subset of (TOP-REAL n) st A is being_line holds
ex p1, p2 being Point of (TOP-REAL n) st
( p1 in A & p2 in A & p1 <> p2 )
let A be Subset of (TOP-REAL n); :: thesis: ( A is being_line implies ex p1, p2 being Point of (TOP-REAL n) st
( p1 in A & p2 in A & p1 <> p2 ) )
assume A is being_line ; :: thesis: ex p1, p2 being Point of (TOP-REAL n) st
( p1 in A & p2 in A & p1 <> p2 )
then consider p1, p2 being Point of (TOP-REAL n) such that
A1: p1 <> p2 and
A2: A = Line (p1,p2) ;
( p1 in A & p2 in A ) by A2, RLTOPSP1:72;
hence ex p1, p2 being Point of (TOP-REAL n) st
( p1 in A & p2 in A & p1 <> p2 ) by A1; :: thesis: verum