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

theorem
  arccos|[.-1,1.] is continuous
proof
  set f = cos | [.0,PI.];
  dom f = [.0,PI.] by RELAT_1:62,SIN_COS:24;
  then f|[.0,PI.] = f & (f|[.0,PI.])"|(f.:[.0,PI.]) is continuous by
COMPTRIG:25,FCONT_1:47,RELAT_1:73;
  hence thesis by COMPTRIG:32,RELAT_1:115;
end;
