let n be Element of NAT ; :: thesis: for V being Subset of (TOP-REAL n)
for t1, s, t2 being Point of (TOP-REAL n) holds t1,s,V -separate t2,s
let V be Subset of (TOP-REAL n); :: thesis: for t1, s, t2 being Point of (TOP-REAL n) holds t1,s,V -separate t2,s
let t1, s, t2 be Point of (TOP-REAL n); :: thesis: t1,s,V -separate t2,s
let A be Subset of (TOP-REAL n); :: according to JORDAN18:def 3 :: thesis: ( A is_an_arc_of t1,s & A c= V implies A meets {t2,s} )
assume that
A1: A is_an_arc_of t1,s and
A c= V ; :: thesis: A meets {t2,s}
( s in A & s in {s,t2} ) by A1, TARSKI:def 2, TOPREAL1:4;
hence A meets {t2,s} by XBOOLE_0:3; :: thesis: verum