reserve r,r1,r2, s,x for Real,
  i for Integer;

theorem Th100:
  -1 < r & r < 1 implies 0 < arccos r & arccos r < PI
proof
  assume
A1: -1 < r & r < 1;
  then arccos r <= PI by Th99;
  then 0 < arccos r & arccos r < PI or 0 = arccos r or arccos r = PI by A1,Th99
,XXREAL_0:1;
  hence thesis by A1,Th91,SIN_COS:31,77;
end;
