theorem Th3:
  sqrt <*r*> = <*sqrt r*>
proof
  set R=<*r*>;
A1: R.1=r;
A2: dom R=dom sqrt R by PARTFUN3:def 5;
  then
A3: len R=len sqrt R by FINSEQ_3:29;
  1 in Seg 1 & dom R=Seg 1 by FINSEQ_1:38;
  then len R=1 & (sqrt R).1=sqrt r by A2,A1,FINSEQ_1:40,PARTFUN3:def 5;
  hence thesis by A3,FINSEQ_1:40;
 end;
