English: So, f n plus 1 minus g is an element of the ideal, if it was not in the ideal generated by f 1 through f n. So, suppose this is not true, suppose what is in this box is not true; that means, this polynomial f n plus 1 minus g is not in the ideal generated by f 1 through f n; that means, it is an I minus f 1 through f n. Because, if it is not in the ideal generated by f 1 through f n it says it is in its complement; that means, it is inside this, but it then because it has smaller degree than f n plus 1 that violates how we chose f n plus 1, because that was supposed to be least degree polynomial in this compliment.
Telugu: కాబట్టి, ఇది నిజం కాదు అనుకుందాం, ఈ బాక్స్ లో ఉన్నది నిజం కాదు అనుకుందాం; అంటే, ఈ పాలినామియల్ f_(n+1) మైనస్ g, f₁ . . . . . . . . f_(n) ద్వారా జెనెరేట్ చేయబడిన ఐడియల్ లో లేదు; అంటే, ఇది I మైనస్ f₁ .