theorem
  frac r = 3/4 implies CircleMap.r = |[0,-1]|
proof
  assume frac r = 3/4;
  then
A1: r-[\r/] = 3/4 by INT_1:def 8;
  thus CircleMap.r = CircleMap.(r+-[\r/]) by Th31
    .= |[ cos(2*PI*(3/4)), sin(2*PI*(3/4)) ]| by A1,Def11
    .= |[0,-1]| by SIN_COS:77;
end;
