Definition divTerm :
  Term A n ->
  forall (b : Term A n) (nZb : ~ zeroP (A:=A) A0 eqA (n:=n) b), Term A n.

Theorem eqT_divTerm_plusTerm : forall (a b c : Term A n) (nZc : ~ zeroP (A:=A) A0 eqA (n:=n) c), eqT a b -> eqTerm (A:=A) eqA (n:=n) a (multTerm (A:=A) multA (n:=n) (divTerm a nZc) c) -> eqTerm (A:=A) eqA (n:=n) b (multTerm (A:=A) multA (n:=n) (divTerm b nZc) c) -> eqTerm (A:=A) eqA (n:=n) (divTerm (plusTerm (A:=A) plusA (n:=n) a b) nZc) (plusTerm (A:=A) plusA (n:=n) (divTerm a nZc) (divTerm b nZc)).