reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;
reserve D for non empty set;
reserve p, q for FinSequence,
  X, Y, x, y for set,
  D for non empty set,
  i, j, k, l, m, n, r for Nat;
reserve a, a1, a2 for TwoValued Alternating FinSequence;
reserve fs, fs1, fs2 for FinSequence of X,
  fss, fss2 for Subset of fs;
reserve F, F1 for FinSequence of INT,
  k, m, n, ma for Nat;

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;
