let X be ComplexUnitarySpace; :: thesis: for x, y being Point of X
for r being Real st y in Ball (x,r) holds
y in cl_Ball (x,r)
let x, y be Point of X; :: thesis: for r being Real st y in Ball (x,r) holds
y in cl_Ball (x,r)
let r be Real; :: thesis: ( y in Ball (x,r) implies y in cl_Ball (x,r) )
assume y in Ball (x,r) ; :: thesis: y in cl_Ball (x,r)
then ||.(x - y).|| <= r by Th40;
hence y in cl_Ball (x,r) ; :: thesis: verum