for f being FinSequence of INT
for m, k1, k, n being Nat st k1 = k - 1 & f is_non_decreasing_on m,k1 & f is_non_decreasing_on k + 1,n & ( for i being Nat st m <= i & i < k holds
f . i <= f . k ) & ( for i being Nat st k < i & i <= n holds
f . k <= f . i ) holds
f is_non_decreasing_on m,n