Fundamental Theorem of Algebra

The following propositions are true: (1) For all natural numbers n, m such that n 6= 0 and m 6= 0 holds (n ·m− n − m) + 1 ­ 0. (2) For all real numbers x, y such that y > 0 holds min(x,y) max(x,y) ¬ 1. (3) For all real numbers x, y such that for every real number c such that c > 0 and c < 1 holds c · x ­ y holds y ¬ 0. (4) Let p be a finite sequence of elements of R. Suppose that for every natural number n such that n ∈ dom p holds p(n) ­ 0. Let i be a natural number. If i ∈ dom p, then ∑ p ­ p(i). (5) For all real numbers x, y holds −(x + yiCF) = −x + (−y)iCF . (6) For all real numbers x1, y1, x2, y2 holds (x1 + y1iCF) − (x2 + y2iCF) = (x1 − x2) + (y1 − y2)iCF . (7) Let L be a commutative associative left unital distributive field-like non empty double loop structure and f , g, h be elements of the carrier of L. If h 6= 0L, then if h · g = h · f or g · h = f · h, then g = f.