let r, s be real number ; :: thesis: for n being Element of NAT
for x being Point of (TOP-REAL n) st r <= s holds
Ball x,r c= Ball x,s
let n be Element of NAT ; :: thesis: for x being Point of (TOP-REAL n) st r <= s holds
Ball x,r c= Ball x,s
let x be Point of (TOP-REAL n); :: thesis: ( r <= s implies Ball x,r c= Ball x,s )
reconsider xe = x as Point of (Euclid n) by TOPREAL3:13;
A1: Ball x,r = Ball xe,r by TOPREAL9:13;
Ball x,s = Ball xe,s by TOPREAL9:13;
hence ( r <= s implies Ball x,r c= Ball x,s ) by A1, PCOMPS_1:1; :: thesis: verum