theorem
  1 <= m & m <= len F implies min_at(F, m, m) = m
proof
  assume that
A1: 1 <= m and
A2: m <= len F;
A3: for i being Nat st m <= i & i < m holds F.m < F.i;
  for i being Nat st m <= i & i <= m holds F.m <= F.i by XXREAL_0:1;
  hence thesis by A1,A2,A3,Th59;
end;
