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 Th8:
  cos(r) = 0 implies ex i st r = PI/2+PI*i
  proof
    assume cos(r) = 0;
    then r = PI/2+2*PI*[\r/(2*PI)/] or r = 3*PI/2+2*PI*[\r/(2*PI)/] by Th6;
    then r = PI/2+PI*(2*[\r/(2*PI)/]) or r = PI/2+PI*(1+2*[\r/(2*PI)/]);
    hence thesis;
  end;
