let X, Y be Subset of TarskiEuclid2Space; for a being Element of TarskiEuclid2Space st ( for x, y being Element of TarskiEuclid2Space st x in X & y in Y holds
between a,x,y ) & a in Y & not X = {a} holds
X is empty
let a be Element of TarskiEuclid2Space; ( ( for x, y being Element of TarskiEuclid2Space st x in X & y in Y holds
between a,x,y ) & a in Y & not X = {a} implies X is empty )
assume that
A1:
for x, y being Element of TarskiEuclid2Space st x in X & y in Y holds
between a,x,y
and
A2:
a in Y
; ( X = {a} or X is empty )
M1:
X c= {a}