theorem Th15: :: BROUWER3:16

for n being Nat
for p, q being Point of (TOP-REAL n)
for r being Real holds
( (transl (p,(TOP-REAL n))) .: (Ball (q,r)) = Ball ((q + p),r) & (transl (p,(TOP-REAL n))) .: (cl_Ball (q,r)) = cl_Ball ((q + p),r) & (transl (p,(TOP-REAL n))) .: (Sphere (q,r)) = Sphere ((q + p),r) )