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

theorem
  arcsin|[.-1,1.] is continuous
proof
  set f = sin | [.-PI/2,PI/2.];
  dom f = [.-PI/2,PI/2.] by RELAT_1:62,SIN_COS:24;
  then f|[.-PI/2,PI/2.] = f & (f|[.-PI/2,PI/2.])"|(f.:[.-PI/2,PI/2.]) is
  continuous by COMPTRIG:23,FCONT_1:47,RELAT_1:73;
  hence thesis by COMPTRIG:30,RELAT_1:115;
end;
