let n be Element of NAT ; :: thesis: for x1, x2 being Element of REAL n
for L being Element of line_of_REAL n st x1 in L & x2 in L holds
Line x1,x2 c= L
let x1, x2 be Element of REAL n; :: thesis: for L being Element of line_of_REAL n st x1 in L & x2 in L holds
Line x1,x2 c= L
let L be Element of line_of_REAL n; :: thesis: ( x1 in L & x2 in L implies Line x1,x2 c= L )
assume A1: ( x1 in L & x2 in L ) ; :: thesis: Line x1,x2 c= L
L in line_of_REAL n ;
then consider L0 being Subset of (REAL n) such that
A2: ( L = L0 & ex y1, y2 being Element of REAL n st L0 = Line y1,y2 ) ;
consider y1, y2 being Element of REAL n such that
A3: L = Line y1,y2 by A2;
thus Line x1,x2 c= L by A1, A3, EUCLID_4:11; :: thesis: verum