reserve n,m for Nat;

theorem Th1:
  for f being real-valued FinSequence,i being Nat st
  1<=i & i<=len f holds f.i<=f.(max_p f) & f.i<=max f
proof
  let f be real-valued FinSequence,i be Nat;
  assume
A1: 1<=i & i<=len f;
  then
A2: i in dom f by FINSEQ_3:25;
  hence f.i<=f.(max_p f) by A1,Def1;
  thus thesis by A1,A2,Def1;
end;
