reserve n,m for Nat;

theorem
  for f being real-valued FinSequence,r being Real st
  f=<*r*> holds min_p f= 1 & min f=r
proof
  let f be real-valued FinSequence,r be Real;
  assume
A1: f=<*r*>;
  then
A2: f.1=r;
A3: len f=1 by A1,FINSEQ_1:40;
  then (min_p f) in dom f by Def2;
  then 1<= (min_p f) & (min_p f)<=len f by FINSEQ_3:25;
  hence thesis by A3,A2,XXREAL_0:1;
end;
