reserve n for Element of NAT,
  i for Integer,
  a, b, r for Real,
  x for Point of TOP-REAL n;

theorem Th34:
  frac r = 1/2 implies CircleMap.r = |[-1,0]|
proof
  assume
A1: frac r = 1/2;
  thus CircleMap.r = CircleMap.(r+-[\r/]) by Th31
    .= CircleMap.(r-[\r/])
    .= |[-1,0]| by A1,Lm19,INT_1:def 8;
end;
