reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

theorem
  SphereMap.i = c[100]
  proof
    thus SM.i = |[cos(2*PI*i+Q),sin(2*PI*i)+Q,0]| by Def6
    .= |[cos(0),sin(2*PI*i+Q),0]| by COMPLEX2:9
    .= c[100] by COMPLEX2:8,SIN_COS:31;
  end;
